Papers

False vacuum decay is conventionally described by a spherically symmetric bounce with a single negative fluctuation mode. This raises a fundamental question: can the single negative mode requirement itself enforce spherical symmetry, independently of action minimization? For a single real scalar field with a smooth potential in flat spacetime, we rigorously prove that every localized nonspherical saddle with zero initial velocity has at least three negative modes. Additional reflection symmetries further tighten these bounds, as illustrated in a sextic scalar model. Our findings exclude nonspherical bounce candidates with a single negative mode, providing a complementary spectral foundation for the spherical bounce description of false vacuum decay.

Recent measurements from DESI baryon acoustic oscillations (BAO) have reported a moderate preference for dynamical dark energy, challenging the standard $\Lambda$CDM paradigm. Nonetheless, such a trend could reflect a tension between the shape and the offset of the Hubble diagrams predicted by current BAO and Type Ia supernovae (SN) data, which may underpin a possible breakdown of the cosmic distance duality relation (CDDR) linking luminosity distances $D_{\rm L}$ and angular-diameter distances $D_{\rm A}$. We explore this possibility by parametrizing deviations from this relation as $\eta(z) \equiv D_{\rm L} / [{(1+z)}^2 D_{\rm A}] = \alpha{(1+z)}^\varepsilon$, and investigate how the preference for a Chevallier-Polarski-Linder (CPL) dynamical dark energy is modified once $\varepsilon \!\neq\! 0$ is allowed. Using DESI DR2 and uncalibrated SN data (Pantheon$+$, DES-Dovekie, Union3, and Union3.1), we find that allowing $\varepsilon$ to vary freely in both $\Lambda$CDM and CPL reduces the CPL preference with respect to $\Lambda$CDM by a larger amount than the addition of spatial curvature $\Omega_k$; only Union3.1 exhibits comparable reductions. We also find that the preference reduction is robust to alternative $\eta(z)$ parametrizations, and that the $\eta(z)$ constraints remain stable under the removal of BAO tracers or low-redshift cutoffs for Pantheon$+$, whereas the DES-Dovekie preference largely disappears once $z < 0.1$ SN are removed. In a separate calibrated analysis, illustrative Planck sound-horizon and SH0ES absolute-magnitude priors give $\alpha \simeq 0.942 \pm 0.014$, quantifying the normalization mismatch under those assumptions. We also map the CDDR violation onto photon-loss and varying-$G$ scenarios, concluding that the cosmological constraints are much weaker than existing constraints on these physical mechanisms.

We study a system of two quadratically-coupled harmonic oscillators, prepared respectively in the ground state and in a coherent state. This toy model can describe for instance the dynamics of one mode of a quantum field evolving in a harmonically-oscillating classical background. In such situations, it is well-known that, depending on the background oscillation amplitude and coupling strength, the system may exhibit parametric resonance. Using the Feynman-Vernon influence functional, we analyze the interplay between parametric resonance and quantum entanglement by perturbatively computing the purity of the mixed state resulting from tracing over one of the oscillators. We find a runaway behavior of the quantum entanglement between the two oscillators, as well as a rapid breakdown of the validity of perturbation theory, in regions of parametric instability. This provides a quantitative confirmation of various statements in the literature and is highly relevant to questions pertaining to the validity of the semiclassical approximation in coupled quantum-classical systems.

The first-order phase transition is central to electroweak baryogenesis and gravitational wave generation, yet thermal equilibrium effective potential analyses cannot describe the real-time non-equilibrium dynamics of the phase transition process. We use the Schwinger-Keldysh closed-time-path formalism of real-time finite-temperature field theory to study these effects. For the $\phi^6$ model, we derive the effective action and the corresponding Langevin equation. We further extend the formalism to the two scalar fields case, obtaining the coupled Langevin equations. These results provide a theoretical framework for the bubble nucleation simulation of the non-equilibrium phase transition process, laying the foundation for reliable predictions of baryogenesis and gravitational wave signals.

We study classical local conserved charges obtained after finite-defect reduction of doubled four-dimensional Chern–Simons theory. At a finite simple zero, the inhomogeneous derivative term in the affine gauge transformation induced by the twist function vanishes, so the residue evaluations of the two Gaudin currents transform by the ordinary adjoint action. For each simple ideal, we use the Evans-compatible invariant tensors of the principal Drinfeld–Sokolov hierarchy as external algebraic input, construct local circle integrals, and treat the same-zero, distinct-zero, and mixed sectors separately, proving pairwise Poisson commutativity. Under the explicit assumptions of Stedman's simple-pole/simple-zero boundary Hamiltonian, the periodic trivial-monodromy sector, and boundary weights independent of phase-space variables, the reduced Hamiltonian decomposes term by term into finite-pole, infinity, finite-zero, and residual first-class-constraint contributions, which yields conservation of the constructed charges. We distinguish the finite-defect reduced space, the extended space carrying the residual constraint, and the physical quotient. The result is a conditional existence statement for a classical local Abelian Poisson subalgebra; we make no claim of functional independence, maximality, or Liouville completeness. Extensions to higher-order zeros and nontrivial monodromy sectors are outside the scope of this work.

We present a nonabelian complex self-dual antisymmetric tensor model, with gauged internal symmetry, comprising a complex multiplet of massless self-dual antisymmetric tensor fields and its conjugate (interacting with massless Yang-Mills gauge fields). We build the model at the classical level, via a first order formulation, assigning local fields to a component expansion over the Dirac algebra and a basis of internal matrices, with Lorentz and gauge invariance ensured by tracing, and applying an appropriate bilinear form. The full expansion requires auxiliary place-holder fields, which are not potentials, but become curvatures (field strengths) after elimination via their algebraic equations of motion. The component expansion over the Dirac algebra is closed under multiplication by additional internal matrices, which are not gauge group generators, but mix internal components, and link auxiliary curvatures with potentials. The model is shown to be invariant under such transformations, and thus possesses a type of hidden internal symmetry. We analyze the specific case of gauge group $SU(2)\! \times \! U(1)$, and as higher symmetry candidates, we consider both the Lie group $SU(3)$ and the Lie superalgebra $SU(2/1)$ (with the additional matrices acting via Lie brackets, or graded Lie brackets, respectively).

We study classical Bopp–Podolsky (BP) electrodynamics on four-dimensional de Sitter spacetime, focusing on its transverse retarded Green function and gauge-invariant electromagnetic response. Because de Sitter spacetime is maximally symmetric, its vector Green functions admit a covariant expansion in a finite basis of invariant bitensors, with scalar coefficients depending only on the invariant separation. For conserved sources, the fourth-order field operator factorizes into Maxwell and massive-vector operators, yielding the BP retarded kernel as the difference of their transverse Green functions. Using the invariant bitensor decomposition, we reduce the propagator equations to a hypergeometric master equation and determine the distributional structure of its solution. The common leading short-distance singularity of the Maxwell and massive-vector sectors cancels, leaving a logarithmic master singularity and a softened vector-potential wavefront. After one curl, the gauge-invariant field-strength kernel contains a null-cone delta distribution and a regular timelike tail. The smooth Maxwell master tail is annihilated by the curl, so the interior electromagnetic tail is generated entirely by the massive sector. We also derive an exact horizon-regular static potential, demonstrate the cancellation of the Coulomb divergence, recover the flat-space BP potential, and formulate the generalized Gauss law. On global de Sitter spacetime, the compactness of the spatial sections requires the total charge to vanish; we implement this constraint using an antipodal charge configuration with smooth factorized initial data. The analysis is classical and does not assume a quantum Lee–Wick contour or a preferred de Sitter vacuum.

We derive the covariant equations of nondissipative chiral hydrodynamics from their equal-time Hamiltonian formulation and identify the Lie–Poisson structure implicit in the chiral brackets. This structure combines fluid motion with local chiral transformations. For a parity-invariant Hamiltonian quadratic in chiral charge densities and pion gradients, without external backgrounds, we derive and solve the constraints imposed by Lorentz boosts. Their coupled nonlinear sector is equivalent to the linear boost transformation laws of a symmetric tensor, which determine the velocity dependence from rest-frame data. For finite, positive rest-frame coefficients, finite ordinary-fluid energy density and thermodynamic derivatives, and a momentum–velocity relation that can be solved in either direction, the chiral Hamiltonian coefficients remain finite at every fluid speed below light speed if and only if the rest-frame pion propagation speed does not exceed the speed of light. This formulation makes symmetry constraints explicit and provides a starting point for future thermodynamically consistent dissipative extensions.

In the canonical Casimir effect, the quantum vacuum is isotropic, and the minimization of vacuum energy drives only a linear attractive force between the plates. However, the introduction of an axion gradient breaks this rotational symmetry. It can be demonstrated that these asymmetric zero-point fluctuations exert a macroscopic mechanical twist on the plates proportional to $\vec{b}^2 \sin (2\vartheta)$ where $\vec{b}$ is the spatial axion gradient and $\vartheta$ is the angle between the axion gradient and the normal to the plates.

Spontaneous symmetry breaking (SSB) is conventionally understood through static vacuum selection in low-energy approximations. However, the nonperturbative dynamical pathways connecting symmetric configurations to asymmetric states remain an open question. In this paper, we propose an operator-theoretic framework that characterizes $Z_{2}$ symmetry breaking in scalar field theory through spectral branching. Specifically, we identify an effective invariant manifold of the nonlinear Klein-Gordon equation termed the "symmetric dual breather mode," whose phase-space geometry is traced using a $t$-dependent finite-dimensional representation. Our analysis demonstrates that static SSB represents merely a small-amplitude limit ($A \ll \phi_{v1}$). As the amplitude increases into the heteroclinic regime ($A > \phi_{v1}$), the field dynamically overflows the central barrier, yielding a vanishing time-averaged order parameter ($\langle \phi \rangle = 0$) and driving a geometric curvature cancellation ($\langle V''(\phi) \rangle_{t} \to 0$). Governed by a universal scaling function $\mathfrak{F}(y)$, the logarithmic period divergence near the heteroclinic boundary naturally generates sub-eV effective mass scales without fine-tuning bare parameters. Furthermore, this dynamic barrier overflow naturally favors Majorana-like self-conjugate states over Dirac-type states. Additionally, nonlinear phase interference along the heteroclinic channel induces asymmetric phase-space contraction, decoupling the right-handed mode and dynamically giving rise to the left-handed Weyl equation. These results bridge nonperturbative wave dynamics, topological mass suppression, chiral selection, and the dynamic origin of active neutrino masses.

We study the role of momentum fractionation in the development of chaos on smooth 3-charge supergravity solutions of D1-D5 theory, specifically momentum-fractionated superstrata. We probe the chaos through the dynamics of null geodesics and waves. On fractionated backgrounds, both geodesics and waves show uniformly strong chaos (large chaotic sea and near-perfect agreement with the Berry random wave hypothesis). In contrast, geodesics and waves on single-mode (non-fractionated) superstrata are closer to separability (although still chaotic). We discuss a possibility that such dichotomy can be related to the expectation that monotone BPS states are less chaotic than fortuitous ones. Finally, we explain why our chaos probes are meaningful for microstate geometries even though they become trivial in the black hole limit.

We give a microscopic derivation of the semi-classical entropy of the black holes of 3d Lovelock gravity with an infinite tower of regularized Lovelock corrections, which include the regular BTZ black holes found recently. Working in the mini-superspace formalism, we show that the reduced action and its boundary term can be obtained in closed form at all orders in terms of the generating function of the couplings. Assuming the ground state is described by the soliton obtained from the static black hole by a double Wick rotation, we compute the soliton mass and reproduce the semi-classical entropy from the Cardy formula without central charges for arbitrary couplings. We then extend the mini-superspace to stationary configurations, compute the mass and the angular momentum of the rotating black holes obtained by a boost, and verify the Cardy formula in the presence of rotation.

Local out-of-time-order correlators (OTOCs) measure the growth of initially small commutators. For bounded local operators, this growth ends when the local commutator becomes of order one, but in an extended system the region over which it is large can continue to expand. We study this spatial proliferation using three related observables: the local squared commutator $C_r(t)$, its spatial sum $\bar C(t) = \sum_r C_r(t)$, and the symmetrically regularised connected dOTOC $D(t)$ of two extensive observables. We show that Lieb–Robinson locality gives $\bar C(t) \lesssim t^d$. We then prove that, in a Gibbs state with uniform exponential clustering, the full dOTOC obeys the same bound, $D(t) \lesssim t^d$, improving our earlier suboptimal $t^{3d}$ bound. We illustrate these results in two quantum many-body systems: a Brownian coupled-cluster model and a finite-temperature SYK chain. In both cases, an exact disorder symmetry relates $D(t)$ to $\bar C(t)$ and allows us to follow the same extensive observable from the pre-scrambling Lyapunov regime into the post-scrambling growth associated with an expanding saturated region. This late-time power-law growth is the concrete realisation of the weak quantum chaos introduced in our earlier work.

Area metrics arise as effective description at intermediate scales in a number of approaches to quantum gravity, including string theory, holography and loop quantum gravity. Recently, it has been shown that area metric actions can be derived from the modified Plebanski framework on the linearized level. Surprisingly these actions avoid extra poles in the propagator for the effective length dynamics, and hence constitute interesting deformations of linearized Einstein gravity. To be able to study whether this property persist for the full theory, we construct here non-linear area metric dynamics from modified Plebanski actions. We provide the geometric tools for area metrics that do not rely on perturbation theory and allow a systematic construction and study of general non-linear area metric actions: an algorithm that extracts a length metric from an area metric and a connection on two-forms that is uniquely determined by the area metric, together with its curvature and curvature invariants. We derive area metric actions from modified Plebanski actions in first and second order versions. We also find that area metric actions can be reformulated as Poincare gauge theories. We determine the effective length metric action, which on a flat background describes a graviton and a massive spin-two field with parity-violating couplings set by the Barbero–Immirzi parameter. Additionally we discuss cosmological backgrounds and the role of the matter coupling, which together open the way to cosmological applications.

A characteristic feature of topological field theories is the absence of local propagating degrees of freedom. In four-dimensional BF theory with cosmological term, we make this feature manifest by exactly reducing the finite non-Abelian shift symmetry. We do so by identifying a higher dressing field, a 1-form compensating the shift, allowing to build from first principles the composite shift-invariant field $\boldsymbol{B}=B-\lambda^{-1}F$. In terms of this dressed field, the dynamics becomes algebraic and sets $\boldsymbol{B}=0$, directly exposing the absence of local propagating degrees of freedom. This provides the first explicit instance of the higher-form Dressing Field Method.

This paper explores topological phase transitions in the momentum space of the $\kappa$-deformed $\phi^4$ lattice model within the mean-field approximation. We show that the double-well structure of the momentum space gives rise to degenerate momentum states at high energies and that this change is marked by a phase transition. We investigate this transition using both numerical and analytical methods, with the analytical approach based primarily on singularity theory. Our numerical analysis shows that the energy at which the topological phase transition occurs is related to the noncommutative parameter by the simple power law $E \sim 1/\alpha^{4}$. By mapping the constant-energy-level surface to the $A_{3}$ singularity, we obtain the same result analytically. We also present results unique to noncommutative systems, showing that the fraction of particles in degenerate momentum states has a nonzero commutative limit. As a nonperturbative effect, this result provides a testable prediction for the existence of noncommutative spacetime.

This thesis investigates the application of techniques developed in supersymmetric gauge theories to physical problems in Quantum Field Theory and Gravity, focusing on the Seiberg-Witten (SW) curve and its quantum version. After reviewing the essential concepts of Supersymmetry and the derivation of the SW curve, we explore its applications in both fields. In Quantum Field Theory, we investigate the emergence of Argyres-Douglas theories in the moduli space of supersymmetric models, focusing on extremal correlators. We analyze a conformal model to compute their instanton corrections, finding agreement with predictions from Effective Field Theory, and discuss the implications for analogous observables in Argyres-Douglas theories. In Gravity, we exploit the quantum SW curve and its relation to differential equations describing physical systems. We establish the linear stability of Topological Stars, arising in the fuzzball proposal, under massive charged scalar perturbations. We also investigate charge superradiance in configurations with a horizon and derive a novel hypergeometric representation of the confluent Heun function, relevant to gravitational-wave propagation in the Schwarzschild background. This result yields a new resummed expression for waveform tail contributions, in excellent agreement with numerical data. Finally, beyond the SW formalism, we develop a Machine Learning algorithm based on Hamiltonian Neural Networks to reproduce the geodesics of a neutral particle in a fuzzball geometry. For critical trajectories, our method outperforms standard numerical integrators in both efficiency and accuracy.

We study dynamical chiral symmetry breaking in $(2{+}1)$-dimensional QED on a rigidly rotating disc, $\Omega R<1$, within the rainbow Schwinger–Dyson framework. At zero temperature the rotation response of the condensate vanishes identically, so $N_c^{\rm SD}(\Omega,T{=}0)=N_c^{\rm SD}(0)=2.60\pm0.01$ (using three operational definitions). At finite temperature, rotation suppresses the condensate through a dominant occupation-reweighting channel, $\hat{\kappa}_{\rm occ}=-1.55$, accounting for $\ge 99.995\%$ of the linearized total response at the reference parameters, with self-consistent feedback amplifying it by $26.5$. The screening channel is reported at fixed regularization, $\hat{\kappa}_{\rm scr}(\varepsilon = 0.01)=-0.97$; its $\varepsilon \to 0$ behavior is logarithmically divergent. The crossover flavor $N^{*}(\Omega)$ falls monotonically at fixed temperature (a corollary). The critical flavor number is unchanged by rotation at $T=0$ (theorem). Together these results set the finite-temperature reference for the model.

The extension of the LUX–ZEPLIN nuclear-recoil analysis to approximately $270\,\mathrm{keV}$ probes a qualitatively new dark-matter regime in which endothermic scattering can suppress conventional low-energy recoils and concentrate the surviving spectrum near the Galactic high-velocity tail. We construct a modular-$S_4$ realization in which a minimal $2N_R+2S$ inverse seesaw accounts for lepton flavor, while a separate pair of Standard-Model-singlet fermions forms the pseudo-Dirac state relevant for high-recoil xenon scattering. The sectors share a common complex modulus $\tau$, so the modular forms selected by charged-lepton and neutrino data also enter the operators generating the dark Dirac mass and Majorana splitting. Our scan yields $181447$ lepton-sector solutions satisfying $\chi^2_{\ell+\nu}<30$, distributed among several disconnected modular regions, and predicts one effectively massless light neutrino at leading order. Restoring the physical scales allows TeV-scale heavy quasi-Dirac neutral fermions with small non-unitarity. We subsequently scan $2\times10^6$ dark-sector points only over flavor-accepted values of $\tau$ and identify common-modulus solutions in the LZ-oriented region $300\,\mathrm{GeV}\le m_\chi\le2\,\mathrm{TeV}$ and $300\,\mathrm{keV}\le\delta\le400\,\mathrm{keV}$. An exploratory two-bin Poisson likelihood, including endothermic xenon kinematics, the Helm form factor, Standard-Halo-Model velocities, Gaussian energy smearing, and profiling over the signal normalization, gives a best grid point at $(m_\chi,\delta)\simeq(1.847\,\mathrm{TeV},371.5\,\mathrm{keV})$, close to the terrestrial inelastic kinematic ceiling. The construction provides a direct link between modular lepton flavor, TeV-scale inverse-seesaw dynamics, and high-recoil inelastic dark matter.

In this paper, we study phase transitions and scalar quasinormal modes(QNMs) of magnetically charged Euler–Heisenberg-dilaton AdS black holes in the extended phase space. We classify the horizon structures for all three signs of the EH coupling and derive the extended first law when the pressure and coupling are varied. For negative coupling, the physical branch exhibits a Van der Waals-like small/large black-hole transition. Using the improved asymptotic iteration method, we find two separated QNM trajectories below the critical pressure, whereas they merge into one continuous curve at the critical point. The GHS limit and the positive couplings considered here do not produce a finite-radius critical point.

We study how a higher-rank classical collective order parameter can select one dominant projective eigenline and, in a $p=2$ realization, support a dynamically autonomous low-energy director sector. In a fully connected projective-rotor model, the collective second moment is a positive semidefinite tensor $T$ of fixed trace. Conventional projective ordering drives its effective rank toward one, selecting a single dominant eigenline. Rank polarization alone, however, does not determine dynamical autonomy: extrinsic-curvature criteria depend on the chosen state-space metric, and the equilibrium tensor does not determine the transverse free-energy Hessian. A two-harmonic model makes this logical independence explicit by producing families with identical $T$ and $r_{\rm eff}$ but different transverse quadratic forms. We then construct rotationally invariant locking interactions that leave a prescribed ordered tensor exactly fixed while increasing every non-Goldstone restoring coefficient as $\Theta(\lambda)$ within a globally controlled stable regime. For a phenomenological inertial realization with a finite positive kinetic matrix, the lowest transverse normal-mode frequency grows as $\Theta(\lambda^{1/2})$; more generally, the low-frequency transverse susceptibility is suppressed as $O(\lambda^{-1})$, including in overdamped dynamics. The construction therefore proves that spectral selection and infrared transverse suppression are independent data. For $p>2$ the selected eigenline has a $(p-1)$-dimensional director manifold; the one-dimensional Goldstone sector used in the dynamical construction is specific to $p=2$. Promoting the selected internal eigenline to a physical clock requires additional soldering and integrability structure.

We review a many-body formulation of gravitational anomalies as obstructions to realizing the complete low-energy data by a local bosonic lattice quantum system of the same dimension. In this formulation, an anomalous theory can be realized at the boundary of a gapped bosonic lattice bulk, whose topological order gives a one-to-one classification of the anomaly. An invertible bulk reproduces conventional anomaly inflow; a bulk with non-trivial topological excitations yields a non-invertible generalization. To describe the holographic theory of anomalies, we explain the distinction between uniquely defined topological order and many versions of topological quantum field theory and discuss the boundary-to-bulk map. As an application of the holographic theory of anomalies, we describe morphisms between local quantum theories (such as quantum field theories). These morphisms are built from a bulk domain wall and an invertible boundary junction, which give rise to a sandwich picture. Chiral boson/fermion theory, Laughlin edges, and boundaries of $\mathbb{Z}_2$ higher gauge theory with bosonic or fermionic point-like excitations illustrate the different kinds of information about non-invertible anomalies contained in transport coefficients, superselection sectors, and condensation data. In particular, a fermionic theory can be viewed as a theory with a particular non-invertible gravitational anomaly. Those examples also reveal that {\it symmetry $\sim$ gravitational anomaly $\sim$ topological order in one higher dimension}.

Low-energy electrons in graphene obey an emergent, rotationally invariant Dirac equation, while the honeycomb lattice enters only through higher-order, symmetry-breaking corrections, the leading one being trigonal warping. This provides a unique solid-state arena to address a cornerstone challenge in quantum gravity: how to detect ultraviolet symmetry-breaking granular corrections, suppressed by a fundamental scale, atop an emergent infrared relativistic continuum. We show that intense counter-rotating $\omega$-$2\omega$ fields and valley-resolved high-harmonic generation (HHG) provide such a probe. Within a family of models that interpolates continuously between the isotropic Dirac cone and nearest-neighbour graphene at fixed Fermi velocity, the valley contrast of the harmonic yield vanishes identically in the symmetric theory, grows linearly with the warping coupling, and its valley-even counterpart appears only at second order, as expected from effective-field-theory power counting. The stronger the laser, the farther it drives electrons from the Dirac points, so the laser intensity plays the role of the collision energy. For the fourth harmonic, the leading warping correction alone accounts for the valley contrast of real graphene up to fundamental intensities of about $10^{11}$ W/cm$^2$, below the damage threshold of monolayer graphene, whereas the fifth harmonic already reveals higher-order lattice corrections at intensities around $10^{10}$ W/cm$^2$. The two harmonics, which rotate in opposite directions, are emitted by opposite valleys. Valley-resolved harmonics are far more sensitive than the residual valley populations, making them a practical detector of lattice-scale physics hidden beneath an emergent Dirac theory.

We study the entanglement structure of gravitons in quasicrystalline inflation. Both parity-even and parity-odd interactions generate graviton pairs with nonzero total momentum. For opposite-helicity pairs with identical momenta, the parity-even contribution can be nonzero, whereas the parity-odd contribution vanishes. The transition from inflation to radiation domination produces additional conventional two-mode squeezing. We derive the resulting normal and anomalous covariances. The initially nonzero reciprocal blocks of the full field-momentum covariance remain nonzero under homogeneous evolution, although individual components can vanish. We show that this homogeneous, helicity-preserving evolution acts unitarily within each helicity sector and therefore preserves the entanglement between the complete right- and left-helicity sectors. Nevertheless, it can eliminate entanglement in the reduced state of a co-propagating pair. We illustrate this distinction using a solvable four-mode model.

Recently, the possibility of having sterile Majorana neutrinos charged under $B-L$ gauge symmetry in the bulk of the dark dimension has been explored. We point out a cosmological restriction on the Majorana mass of bulk neutrinos leading to mass $\gtrsim 100~{\rm GeV}$. This avoids the over-production of Kaluza-Klein neutrino towers in the early universe thus resolving the cosmological neutrino catastrophe of extra dimension scenarios. If the mass of the bulk neutrino is at the lower end of this bound, it can potentially also explain the recently observed Fermi halo excess on gamma rays through the evaporation of long-lived 5d (i.e. dark) black holes through Hawking radiation to bulk neutrinos, which promptly decay into standard model particles.

We study electrically charged black branes in four-dimensional Einstein-Maxwell-scalar theory with Maxwell coupling $Z(\phi)=e^{3\phi/\sqrt7}$, whose potential has an AdS$_4$ fixed point only in the infrared. For nonzero hair parameter $\alpha$ the scalar grows logarithmically at large radius and the geometry is not asymptotically AdS, so the holographic dictionary is a working assumption. With the scale-invariant multi-trace boundary condition of the neutral branes, giving conformal thermodynamics, we work to second order in the charge, obtaining the Maxwell field and susceptibility in closed form, plus the thermodynamics, condensate, incoherent conductivity and cumulant ratio $T^2\chi_4/\chi_2=6c(\alpha)<0$ for all $\alpha$ considered. Independent perturbative computations and first-law closed forms agree within $4\times10^{-6}$; nonlinear solutions reproduce second-order results to $1.2\times10^{-5}$ and $c$ to $6\times10^{-4}$. They are locally thermodynamically stable where constructed, and the pressure is analytic in $(\mu_Q/T)^2$ near zero density. No regular extremal horizon exists at finite scalar value, and $\rho/s<\sqrt{21}/(2\pi)$ exactly. The extremal limit is an AdS$_2\times\mathbb R^2$ throat where the scalar grows as $\ln\ln(1/u)$ in the AdS$_2$ radial coordinate $u$; the bound is saturated there, and extremal values are approached as powers of $1/\ln(\mu_Q/T)$. With a Dirichlet condition on the scalar source, the same solutions describe a non-conformal theory with scale $\Lambda$, whose charged branes exist only below $T_{\max}(\mu_Q)$, which falls from $0.194\Lambda$ at zero density to zero at $\mu_Q=0.506\Lambda$. This boundary is a diffusive instability where the charge susceptibility diverges at nonzero density, and the bulk viscosity violates Buchel's bound at all densities. Quasinormal modes with the normalizable large-radius condition reproduce its hydrodynamics.

The energy densities of the quantised scalar and electromagnetic fields need not be positive, but their averages along timelike worldlines are constrained by Quantum Energy Inequalities (QEIs) that hold in flat and curved spacetimes for arbitrary Hadamard quantum field states. However the general QEI bound is not easy to compute in closed form. Here, we compute closed form expressions for the massless scalar and electromagnetic fields along stationary worldlines in Minkowski spacetime. These worldlines are solutions to the four-dimensional Frenet-Serret equations with constant curvature invariants and include inertial, uniformly linearly accelerated, and uniformly rotating worldlines as special cases. The QEI bound depends on a choice of tetrad along the worldline, and we compute it for any tetrad with constant angular velocity relative to the Frenet-Serret tetrad. Optimising over the angular velocity, we show that the tightest electromagnetic QEI bound occurs when the tetrad is invariant under Fermi-Walker tetrads. Surprisingly, the Fermi-Walker tetrad does not produce the tightest QEI bound for massless scalar fields, and we investigate the optimal bound both analytically and numerically. Our results and methodology significantly improve on those in [CJ Fewster & J Thompson, Class. Quantum Grav. 40 (2023) 175008], in which only Frenet-Serret tetrads were considered for massless scalar fields.

Gauging fermion parity in a $(2+1)$-dimensional fermionic topological order requires lifting its symmetries to the resulting bosonic theory. We give a direct tensor-categorical proof that, for a slightly degenerate braided fusion category $\mathcal{C}$ and a fixed minimal nondegenerate extension ${\cal E}$, the restriction homomorphism $r\colon\operatorname{Aut}_{\mathrm{LR}}(\mathcal{E})\to \operatorname{Aut}_{\mathrm{LR}}(\mathcal{C})$ on classes of complex-linear locality-respecting (LR) braided autoequivalences is surjective with central kernel $\mathbb{Z}/2$, generated by fermion attachment. Thus each symmetry class has exactly two LR lift classes, related by attaching the fermion to every vortex. We apply graded Morita theory to reduce the kernel to two module types on the vortex sector, corresponding to tensoring with the vacuum or the fermion. We then prove relative rigidity to show that each type determines a unique LR class, which are distinguished by fermionic self-braiding even when their actions on simple-object labels coincide. We prove surjectivity by extending graph algebras in $\mathcal{C}^{\mathrm{rev}}\boxtimes\mathcal{C}$ to Lagrangian algebras in $\mathcal{E}^{\mathrm{rev}}\boxtimes\mathcal{E}$. Our results require neither unitarity nor a ribbon structure. We illustrate the lifting ambiguity in the Laughlin state, the $SO(3)_3$ theory and the Ising topological order.

We show that gravity can remove the linear magnetic instability of a holographic plasma with an $SU(2)$ global symmetry. In the probe limit, charged vector bosons become tachyonic in their lowest Landau level above a critical field and condense into a vortex lattice. In Einstein-$SU(2)$ Yang-Mills theory in AdS$_5$ we include the backreaction of the field exactly, expanding only in the condensate around the D'Hoker-Kraus magnetic brane. The critical field diverges as the coupling $\alpha = \kappa^2/\hat g^2$ approaches $\alpha_\star = 2/3$, above which the normal phase has no linear charged instability at any field or temperature: we show this at zero temperature and establish it numerically at finite temperature. At zero temperature the field cancels from the mass of the lowest Landau level in the brane's AdS$_3 \times \mathbb{R}^2$ throat, and the instability is a violation of the throat's Breitenlohner-Freedman bound. The onset temperature vanishes at $\alpha_\star$ with an essential singularity of Berezinskii-Kosterlitz-Thouless type. For two-derivative Einstein-Yang-Mills duals in $d = 4$, 5 and 6 dimensions the normal phase has a charged instability if and only if $C_J/C_T < 8/(d^2(d+1))$, one tenth in $d = 4$. Above $\alpha_L = 0.372$ the gravitational attraction between vortices makes the uniform lattice unstable and the transition first order, so $B_c$ is only a spinodal; whether a condensed phase survives above $\alpha_\star$ is left open.

We derive Bondi four-momentum balance between past and future null infinity in the radiative phase space of the null-surface formulation (NSF). Weyl matching at spatial infinity, together with vanishing endpoint News, gives antipodal continuity of the Bondi mass aspect. Its translation projection is independent of the infrared shear term and transforms as a Lorentz four-vector. Bondi evolution relates the incoming and outgoing News fluxes to the timelike endpoint momenta; in the Dominguez–Kozameh–Ludvigsen radiative sector these momenta vanish and the fluxes are equal. On a common radiative Fock domain, unitary conjugation transports the flux observables. Adopting their classical balance as an additional quantum condition yields exclusive four-momentum conservation. We also calculate the outgoing energy expectation without imposing that condition. For an incoming energy eigenstate, the second-generator commutator vanishes diagonally, leaving a second-order coefficient determined by the cubic generator. Direct canonical contractions isolate the contribution connected to all four external legs. For the equal-energy center-of-mass preparation, axial rotational covariance forces the angularly integrated exchange coefficient to vanish under the finite helicity-projection prescription of Part~I. The connected energy defect therefore vanishes through second order. The full expectation (including spectators) and higher-order balance remain open.