Papers

In this paper, we discuss the conjugate boundary condition (CBC), which has recently been studied as a way of realizing a Majorana fermion within a compactified five-dimensional theory ($\mathcal M^4\otimes S^1/Z_2$). The Majorana fermion which plays a crucial role in the seesaw scenario arises as a zero mode (lowest mode) by imposing the CBC. Although each nonzero Kaluza-Klein (KK) mode is also naively expected to be described by two Majorana fermions, we show by direct calculation that they can be combined into a Dirac spinor in the free theory or up to the level of the quadratic term in the Lagrangian. This difference comes from the fact that an accidental U(1) symmetry exists in the KK mode sector, though such a symmetry does not appear in the zero mode sector. We also point out that the compatibility between the CBC and the axial U(1) transformation plays a crucial role in the diagonalization of the KK mode. We also investigate interactions compatible with both the CBC and the chiral orbifold projection. We find that a nontrivial bulk interaction between a CBC fermion and a chiral-orbifold fermion is allowed. As an application, we construct an extended seesaw scenario by utilizing both boundary conditions and such nontrivial bulk interactions. The resulting seesaw scenario has a different property in contrast with the conventional extended seesaw scenario; namely, the above new non-trivial interactions cause lepton number violation (LNV), while the Majorana mass term in our model does not violate lepton number.

Recent analyses of Proca theories with non-minimal curvature couplings have uncovered an additional scalar degree of freedom with an identically vanishing propagation speed, $c_s^2=0$, signaling a scale-dependent strong-coupling problem. In this Letter, we show that an additional derivative interaction can lift this zero-speed degeneracy and restore a non-degenerate quadratic dynamics for the scalar perturbations. In an open region of parameter space, the scalar kinetic matrix is positive definite and the high-frequency propagation speeds are real and positive. At quadratic order, this removes the specific signature of strong coupling associated with the $c_s^2=0$ mode. We also uncover a non-uniform limit as the temporal vector condensate approaches zero: at fixed nonzero $A_0$, the formal extreme-ultraviolet regime develops a ghost, while the kinetic structure of the exactly vanishing-condensate branch is different. The momentum scale at which this ghost appears is pushed toward increasingly high values as $A_0\to0$. Whether the ghost scale ultimately lies above the EFT cutoff depends on an independent determination of the EFT cutoff. Finally, we identify a stable de Sitter fixed point with $A_0\neq0$, surrounded by a finite region in which the scalar no-ghost and high-frequency stability conditions remain satisfied.

We consider the classical satellite and splice constructions of knot theory from the perspective of link-complement states in three-dimensional topological quantum field theory (TQFT). These states are prepared by a TQFT on a link-complement manifold, namely a manifold with multiple disjoint torus boundaries, obtained by removing a thickened link from a closed ambient three-manifold. In this setting, satellite and splice constructions are realized by gluing manifolds along torus boundaries, and the TQFT assigns to these building blocks multilinear operators acting on the corresponding torus Hilbert spaces. We give explicit prescriptions for these operators and show how they can be used to build link-complement states. This construction is closely related to the JSJ decomposition of link-complement manifolds. While splicing builds manifolds by gluing along tori, the JSJ decomposition cuts a manifold along essential tori into canonical pieces. From the TQFT point of view, this expresses a link-complement state as a network of elementary operators associated with the JSJ pieces. We illustrate this framework by studying the entanglement entropy of Seifert-fibered link complements, Hopf-chain complements, and complements of Whitehead-doubled Hopf chains, showing how their different JSJ structures lead to distinct entanglement patterns.

It is widely believed that global symmetries cannot exist in a consistent theory of quantum gravity. A prominent mechanism underlying this expectation is provided by gravitational instantons or Euclidean wormholes, whose contributions to the Euclidean path integral generates local symmetry-breaking operators in the effective action with couplings parametrized by the $\alpha$-parameters $\overrightarrow{\alpha}=(\alpha_1^{},\alpha_2^{},\cdots)$. The appearance of these $\alpha$-parameters is often taken as evidence that wormholes explicitly break global symmetries. In this paper, we argue that this conclusion is premature. The fate of the symmetry is determined by the ensemble average over these $\alpha$-parameters. We show that, under broad situations, this average can be sharply dominated by the symmetric point $\overrightarrow{\alpha}=0$, while contributions from other symmetry-breaking critical points $\overrightarrow{\alpha}\neq 0$ are typically suppressed by a doubly exponential factor $\exp(-e^{2S_{\rm ins}})$, where $S_{\rm ins}$ is the instanton action. In particular, standard $\mathrm{U}(1)^{}$ Peccei–Quinn models fall into this class, implying that the conventional axion quality problem does not arise in the wormhole-induced effective theory. Our analysis is formulated for general $\mathrm{U}(1)^{}$ $p$-form global symmetries.

I develop a Hamiltonian framework for ${\mathbb Z}_k$ $p$-form gauge fields on arbitrary oriented cell complexes in arbitrary dimensions. Gauge qudits are defined by $p$-cells, charged boundary qudits by $(p-1)$-cells, Gauss-law generators by boundary map $\partial_p$, and magnetic checks by $\partial_{p+1}$. The same cellular structure produces local dressed Wilson operators, and at $k=2$ a Calderbank-Shor-Steane check complex relevant to quantum error correction. I then specialize to $p=2, k=2$, where the magnetic 3-cell term is absent and the one-form Gauss-law can be solved exactly. The physical Hilbert space is parameterized by plaquette electric-flux variables, while the link configuration is reconstructed as the dynamical boundary of the evolving flux domains. The reduced Hamiltonian is an Ising-type plaquette model, where its local transverse-field term is the physical image of the boundary-dressed Wilson operator $\sigma_p^z\prod_{\ell\in\partial p}\tau_\ell^z$. A tube-cap quench compares two initial flux fillings with the same initial boundary loops. Exact diagonalization on $4\times4$, $6\times4$, and $5\times5$ tori finds that the cap loses $20$-$37\%$ of its occupied-flux area, while the tube remains nearly pinned. A finite-size scaling locates a dynamical crossover of tension-to-density ratio near $(m/\varepsilon_E)_c\simeq1.89$. The unreduced plaquette-plus-link encoding provides local Gauss-law checks and a direct digital implementation, while the reduced plaquette-only Hamiltonian supplies the exact benchmark. The result places the specific top-form discharge and the cosmological constant neutralization calculation inside a general higher-form Hamiltonian and coding framework.

Krylov complexity is a powerful diagnostic of quantum dynamics, with clear connections to other measures of quantum chaos and operator growth. One such measure is the Loschmidt amplitude, defined as the overlap of initially identical states evolved under two slightly different Hamiltonians. Its decay in certain systems is controlled by the classical Lyapunov exponent. Using the algebraic properties of the Krylov complexity operator, we express Krylov complexity as the derivative of a Loschmidt amplitude whose perturbation is parameterized by an angular variable $\phi$. This formulation allows us to define a spectral propagator that encodes the entire complexity distribution, which we characterize for specific types of systems. We study the two-dimensional quantum geometry spanned by time and $\phi$ where the original and deformed trajectories reside, demonstrating that Krylov complexity is upper-bounded by its volume. We also express the time derivative of Krylov complexity in terms of a distinct Loschmidt amplitude. Depending on the growth of the Lanczos coefficients, the perturbation term in this amplitude can be truncated. We propose that the strength of this perturbation provides a classification scheme for Krylov complexity dynamics and relate it to the $\phi$-derivative of the spectral propagator. Using this analytical framework, we derive general relations between the time-dependence of the survival amplitude and Krylov space measures.

The one-loop effective Lagrangian of quantum electrodynamics for dyons (dQED) with a $U(1) \times U(1)$ gauge symmetry is derived using the Schwinger proper-time method. We identify the analog of the Schwinger pair-production limit and compute the corresponding nonlinear equations of motion. The electromagnetic response of the model is analyzed by linearizing the equations of motion around a purely magnetic background. From the resulting plane-wave solutions, we obtain the effective permittivity and permeability tensors, along with the associated dispersion relations and refractive indices for parallel and perpendicular polarization modes. The refractive indices involve hybrid superpositions of both gauge sectors, as illustrated in the symmetric case $q_{(1)} = q_{(2)}$. In this background, the model exhibits vacuum birefringence, indicating that the quantum vacuum behaves as an anisotropic medium. All results consistently reduce to the standard Euler-Heisenberg predictions of QED when the magnetic charge vanishes.

Jordan pairs and hermitian Jordan triples were discovered by mathematicians studying Jordan algebras, which describe the possible algebras of observables in quantum mechanics. We point out a striking correspondence between the doubly exceptional hermitian Jordan triple (the so-called “bi-Cayley” triple) and the structure of the Standard Model of particle physics. We also point out how ordinary quantum mechanics may be reformulated, and generalized, using hermitian Jordan triples.

We construct a new family of asymptotically flat static and rotating regular black holes characterized by a Minkowskian core and a finite two-horizon structure. The solutions are obtained within the framework of gravitational decoupling and provide an analytically tractable realization of non-singular black hole geometries with a regular interior and well-defined asymptotic properties. We investigate the optical appearance of the rotating spacetime through shadow observables and ray-traced images of geometrically thin, optically thin accretion disks. Despite the substantial differences between the interior geometry of these solutions and that of singular black holes, their optical signatures are found to remain remarkably close to those of Schwarzschild and Kerr spacetimes with the same asymptotic parameters. Our results show that markedly different black hole interiors may lead to nearly indistinguishable optical appearances, highlighting the challenges of probing the internal structure of compact objects using current shadow and imaging observations.

We study a four-qubit product-EPR holographic code whose reconstructing region contains matter and one leg of a geometry bond. Seven deformations compare local, bipartite, bond-stabilizing, and bond-moving operators. Exact spectra show that only matter-controlled bond motion produces a leading quadratic logical-state dependence of the boundary entropy. We select one state-independent physical recovery by optimizing coherent information of the channel Choi state. A separate semidefinite program maximizes entanglement fidelity over all channels. At fixed coupling the physical recovery attains that optimum to numerical precision, while recovered-entropy subtraction leaves a nonzero variational proto-area response. Total stabilizer Renyi magic is also nonzero for deformations with no boundary response, so it does not characterize the effect. Projecting the exact stabilizer-Renyi quadratic form away from pairwise Pauli tangents defines a leading-order boundary witness. Its global convex minimum is positive for the bond-moving deformation and zero for the six comparisons. For the reference-matter-geometry resource partition, however, pairwise tangents span the full projective tangent space at the product-EPR base, so the witness vanishes for every Hermitian deformation. A two-bound extension retains this degeneracy but exhibits a split-geometry structural residual and a logical-state-dependent cut switch. These results establish a finite-code witness, not a universal magic law or continuum gravitational dynamics.

A photon coupled non-minimally to the Weyl tensor propagates differently in its two linear polarization states: the vacuum around a black hole becomes a birefringent medium. On a Schwarzschild background the coupling $\alpha$ splits the photon sphere and the critical impact parameter of the two polarizations, producing a double shadow and a polarization-dependent photon ring; the two shadow edges separate by $62\%$ of the shadow radius at $\alpha/M^2=0.75$. We compute a unified set of wave-optical and geometric-optical observables for both polarizations across a range of $\alpha$: greybody factors, absorption cross sections, differential cross sections and their glories, a backward birefringence signal, shadows, photon rings, and null trajectories. The two-polarization scattering matrices are extracted with a Riccati–Hankel matching scheme that keeps the phase-sensitive observables reliable, and the geometric-optics chain is cross-validated with three independent ray tracers. The cleanest diagnostic is the backward signal: it is protected by parity and vanishes identically at $\alpha=0$.Laboratory bounds on $\alpha$ render these effects unobservable for supermassive black holes; order-unity couplings would require a black hole of primordial mass.

Determining whether Planck-scale effects can stabilize black holes addresses fundamental questions about black hole evaporation and quantum gravity consistency. Here, we analyze the thermodynamic topology of Schwarzschild black holes under Planck-scale modified kinematics, using a cubic entropy correction derived from a well-known phenomenological MDR with leading correction \(\eta E^3/E_P\). Enforcing physical constraints (\(S'(r_h) > 0\), \(T > 0\)) via the entropy-geometry correspondence, we find a single unstable branch with \(w = -1\) and \(W = -1\) for both signs of the correction parameter. A second root suggesting stability (\(w = +1\)) is excluded due to negative mass/temperature and lies outside the perturbative regime. Thus, this class of MDRs does not yield stable Schwarzschild black holes. However, MDRs with different leading-order corrections may behave otherwise, leaving the search for Planck-scale stabilization an open endeavor.

We develop a microscopic quantum membrane paradigm from the matrix quantum mechanics of black holes [1]. It was proposed that a quantum black hole is described by a fuzzy sphere together with a half-filled Fermi sea of horizon partons. We show that the topology of the fuzzy sphere induces a Berry monopole, providing a microscopic origin for the monopole appearing in the tunneling description of the decay of quantum black hole. Because the partons couple to the fuzzy sphere as fundamental degrees of freedom, they are sensitive to this monopole and form Lowest-Landau-Level (LLL) states rather than ordinary propagating two-dimensional fermions. Their guiding-center dynamics generates Ohmic, Hall, and polarization currents on the horizon. To couple these currents to an external electromagnetic field, we introduce a two-block matrix configuration comprising black-hole, environmental, and bifundamental link sectors. Off-diagonal link modes become tachyonic near the fuzzy sphere and condense, dynamically locking the horizon gauge field to the boundary value of the external Maxwell field. The parton current thereby becomes a physical boundary source for the exterior field. Our construction replaces the fictitious membrane of the classical paradigm with a dynamical quantum membrane populated by microscopic LLL degrees of freedom. The resulting boundary condition generalizes the classical ingoing membrane condition and yields explicit quantum, frequency-dependent, and helicity-dependent corrections, offering a possible probe of the microscopic quantum structure of the horizon.

We study the response of axion topological materials under the presence of external static electric and magnetic fields. We focus on the macroscopic quasi-static magnetoelectric response of topological insulators. We use techniques based on surface variables that have been previously employed in soft condensed matter problems for the description of heterogeneous systems composed of multiple homogeneous materials. A complete description of the whole system is written in terms of surface degrees of freedom, which in this case correspond to effective surface charge and surface current densities. We obtain a set of integral equations satisfied by these variables. We present exact analytic solutions for axial-symmetric cases. We develop a numerical method for the solution of the integral equations by means of a boundary finite element method. We apply the numerical method to topological insulators with different geometries such as spheres, hollow spheres and toroidal surfaces. We show that that a variational principle can be used to recover the surface variables equations.

We investigate Krylov spread complexity for states evolving under time-dependent Hamiltonians. For periodically driven systems, we formulate the problem within Floquet theory and show how the Magnus expansion provides a systematic approximation when the Floquet Hamiltonian is not available in closed form. We then extend this framework beyond periodic driving and demonstrate that, in addition to the globally truncated Magnus expansion, a piecewise Magnus expansion provides a reliable method when the global expansion loses convergence or accuracy. Our results provide practical tools for analyzing complexity growth in a broad class of time-dependent quantum systems.

We proceed to construct a non-Abelian dual pair for the $AdS_2 \times H^2 \times H^2$ background by applying the non-Abelian T-duality (here as Poisson-Lie T-duality on a semi-Abelian double). By using a certain parameterization of the $6$-dimensional Lie group ${A}_2 \otimes {A}_2 \otimes A_2$ we construct the original $\sigma$-model including the $AdS_2 \times H^2 \times H^2$ metric in the absence of $B$-field. It is shown that the dual background constructed by means of the Poisson-Lie T-duality is supported by a $B$-field and a metric whose contains a physical singularity. By studying the behavior of the dual spacetime at small $(r , y, u)$ coordinates, we show that the dual metric with a zero field strength and a non-trivial dilaton field make up a solution for the vanishing of the one-loop beta-function equations. Furthermore, at large $(r , y, u)$, it is shown that the $AdS_2 \times H^2 \times H^2$ solution is preserved under the non-Abelian T-duality. Finally, using the duality map obtained from the canonical transformation description of the Poisson-Lie T-duality for the gluing matrix which locally defines the properties of the D-brane, we find seven different cases of the gluing matrices for the $AdS_2 \times H^2 \times H^2$ $\sigma$-model and its dual pair. In this way, it is found a symmetric duality action on the branes linking together in a duality chain.

We study the motion of massive (un)charged test particles in space-times of electric and dyonic black holes which carry scalar hair. We determine the stable and unstable circular orbits and discuss the collision of massive test particles. In particular, we aim at demonstrating how the presence of the scalar hair of the black hole changes the circular orbits and particle collisions, respectively, as compared to the Reissner-Nordström (RN) space-time. We find that in the presence of scalar hair, up to four circular orbits (two unstable and two stable) as well as static orbits with $L=0$ can exist. Particle collisions can generate infinite center-of-mass energy when at least one of the particles is charged, very similar to the RN case. We find, however, that the value of the charge at which this divergence happens depends on the value of the scalar field on the horizon.

Anyons in $2+1$ dimensions are not only characterized by exotic braiding statistics but also by intricate fusion properties. Two anyons may fuse into multiple topological charge sectors, and associativity of fusing three anyons to produce a fixed charge sector is governed by $F$-symbols. While braiding invariants, such as the modular data, are typically complex valued, a complete description of general anyon models requires understanding the arithmetic properties of its fusion associativity data as well. The $F$-symbols for many of the most common $2+1$d topological orders, including all Abelian anyon models as well as Fibonacci and Ising anyons, can be made real valued. We show this phenomenon is not universal by exhibiting braided fusion categories whose $F$-symbols cannot be made real. We call such $F$-symbols "inherently complex." The examples we study lack a charge-conjugation symmetry and our results are therefore consistent with the converse of a statement proved in a companion work linking real $F$-symbols in braided fusion categories with the existence of a suitable charge-conjugation symmetry. We analyse the smallest-rank braided fusion categories we know of with inherently complex $F$-symbols: ${\rm Rep}(\mathbb{Z}_7\rtimes\mathbb{Z}_3)$ and ${\rm Rep}(\mathbb{Z}_5\rtimes\mathbb{Z}_4)$. Consequently, the corresponding $\mathcal Z({\rm Rep}(\mathbb{Z}_7\rtimes\mathbb{Z}_3))$ and $\mathcal Z({\rm Rep}(\mathbb{Z}_5\rtimes\mathbb{Z}_4))$ anyon models also have inherently complex $F$-symbols. Our presentation connects these examples with recent results on classifying anyons beyond modular data.

We show that relativistic theories with purely relaxational excitation spectra, such as kinetic theory and transient hydrodynamics, naturally endow the dispersion plane $\{i\omega,ik\}$ with a Lorentzian geometric structure analogous to that of the Minkowski plane $\{t,x\}$. In this picture, timelike future-directed, timelike past-directed, and spacelike directions correspond respectively to relaxation-like, unstable-like, and evanescent-like modes. Under mild structural assumptions on the underlying theory, causality constrains dispersion relations to follow spacelike trajectories on the plane. This geometric viewpoint recasts longstanding problems in relativistic matter physics as elementary geometric ones that can often be solved graphically. As applications, we derive universal constraints on dispersion relations, deviations from time dilation, the observer dependence of spectral hierarchies, the regime of validity of hydrodynamics in boosted frame, the maximal allowed diffusivity and viscosity of relativistic media, and the presence of non-hydrodynamic branch cuts in kinetic theory.

We use the auxiliary polarization spinor formalism together with superspace techniques to construct a complete and minimal list of 3-point invariant structures in three-dimensional superconformal field theories (SCFTs) with $\mathcal{N}=3$ and $\mathcal{N}=4$ superconformal symmetry. The existence of non-abelian $R$-symmetry for $\mathcal{N}=3,4$ gives rise to novel invariant structures built from the antisymmetric invariant tensor. These invariants are used to enumerate the structural form of spinning 3-point correlators of general as well as conserved spinning superfield operators in 3d SCFTs. For conserved operators, we find that the $\mathcal{N}=3$ correlators are fixed upto one parity-even and one parity-odd structure, while $\mathcal{N}=4$ conserved correlators admit two parity-even structures and one parity-odd structure, with the second parity-even structure associated with mirror symmetry breaking.

We compute the fermion-photon vertex in QED in the presence of a constant and uniform magnetic background up to one-loop order. We show that even at tree-level, the vertex is modified due to the loss of Lorentz invariance induced by the magnetic field, thus breaking into longitudinal and transverse pieces. Moreover, the radiative corrections induce the emergence of a rich tensor structure that includes the anomalous magnetic moments in the transverse, parallel, and mixed transverse/parallel directions. We concentrate on studying one of these anomalous magnetic moment components, the one in the purely transverse direction. We find the selection rules for transitions between a few low-lying Landau levels and show that the amplitudes for transitions from an initial to a final Landau level differ by a sign from the reverse process due to the loss of time reversal invariance induced by the presence of the field. Contrary to the vacuum case, the amplitudes are, in general, complex, and the phase factor can be interpreted in terms of a finite life-time of the decaying state. For the anomalous magnetic moment in the purely transverse direction, transitions between states occupying both the lowest Landau levels are forbidden. Moreover, for the computation of the allowed transitions, we find that it is not necessary to include a photon mass since the magnetic field acts as an infrared regulator.

Bern-Carrasco-Johansson relations are helicity-independent constraints among the partial amplitudes of tree-level processes containing gluons and possibly also matter fields. They are a consequence of color-kinematic duality, but alternatively can be derived using the color-factor symmetry of tree-level amplitudes. We use recursive perturbiner methods to present a general, streamlined proof of the color-factor symmetry of all tree-level amplitudes containing an arbitrary number of fundamental spin-zero or spin-one-half matter fields and at least one gluon.

We study scalar and vector bosons in the Bonnor–Melvin–$\Lambda$ spacetime within the Duffin–Kemmer–Petiau (DKP) formalism. By employing Umezawa's projection operators, we separate the physical spin-0 and spin-1 sectors and derive the corresponding exact second-order equations in the full curved spacetime, without relying on the conical approximation. For the scalar sector, the radial equation reduces to a Schrödinger-like equation with a trigonometric Pöschl–Teller effective potential. In the vector sector, the longitudinal mode is governed by the same effective potential, whereas the transverse polarizations are described by generalized trigonometric Pöschl–Teller potentials. Because the me\-tric function vanishes at a discrete set of radial points, the radial dynamics is naturally formulated as a singular Sturm–Liouville problem on a fundamental interval, with the physical radial domain fixed by the Friedrichs self-adjoint extension of the corresponding singular radial operators. As a result, all physical sectors exhibit purely discrete radial spectra, and their eigenfunctions are obtained in closed form. These results provide a unified exact treatment of scalar and vector bosons in the Bonnor–Melvin–$\Lambda$ spacetime, complement previous analyses based on the conical approximation, and clarify the role of the global geometric structure of the background in shaping confinement and spectral properties.

Extra-dimensional QCD axion is well motivated by string compactifications and enjoys enhanced protection against quality-violating effects. If present during inflation, however, its quantum fluctuations generate isocurvature perturbations that strongly constrain the inflationary scale. We propose a dynamical suppression mechanism in warped five-dimensional models, where a radion-inflaton coupling sets the radion minimum at small inter-brane separation during inflation, temporarily enhancing the effective four-dimensional axion decay constant. After inflation, the radion minimum shifts to larger separation, restoring the standard QCD axion window. In a warped orbifold GUT with Goldberger-Wise stabilization, this mechanism can satisfy CMB isocurvature bounds while allowing substantially higher inflationary scales than in conventional pre-inflationary axion cosmology.

Thanks to bosonization, bosonic lattice models can offer a lattice regularization of chiral fermions. We construct chiral lattice fermion operators in the 2D modified Villain scalar model and evaluate their correlation functions. This microscopic bosonic model has an ultra-local action and an ultra-local symmetry that realizes the fermionic chiral symmetry under bosonization. The reconstructed lattice Dirac operator has no doublers, but is consistent with the Nielsen-Ninomiya theorem because it turns out to be non-local. The non-locality of this derived quantity at finite lattice spacing does not pose any obstructions to gauging the non-anomalous symmetries of the model, which is itself ultra-local.

We show that solving the abelian part of the local anomaly cancellation conditions for a 4-d gauge theory whose gauge Lie algebra has an abelian summand with rank $K \geq 1$ is equivalent to the problem in algebraic/arithmetic geometry of finding $(K-1)$-dimensional projective linear subspaces of a cubic hypersurface over the rational numbers, where the cubic is determined by the data of the semisimple summand and the representation thereof carried by the Weyl fermions. We then use this reformulation to solve a variety of examples with rank 2. The simplest non-trivial example from physics, namely gauge Lie group $U(1)^2$ and six fermions, nevertheless has a rich (and well-studied) geometry: it corresponds to the Fano variety of lines in the Segre cubic primal threefold. This is a surface with 15 irreducible components that are planes (which correspond to lines lying in the 15 planes in the Segre cubic primal and which give rise to non-chiral fermions) and 6 components that are split del Pezzo surfaces of degree 5 (which give rise to chiral fermions). These components are all rational varieties, enabling all solutions to the anomaly cancellation conditions to be parametrized and their collective properties (e.g. their topology and asymptotic distribution) to be described.

The established $d=5$ ALP effective Lagrangian describes the interaction of scalars with approximate shift-symmetry which carry no Standard Model (SM) charges with SM fields. It implicitly assumes that ALPs are not charged under any symmetries of the dark sector. In this paper, we remove this assumption. For ALPs carrying conserved dark charges, no $d=5$ ALP effective interaction to SM particles is possible. We build the effective Lagrangian for these darkly charged ALPs stemming from a general breaking pattern, and we show that the lowest-order shift-symmetric effective Lagrangian contains just two $d=6$ operators coupling ALPs to SM particles. We explore the model-independent phenomenological implications of these interactions, as well as the question of whether the dark matter observed in the Universe may consist of darkly charged ALPs. We identify higher order operators of the effective field theory, and determine which types of dark symmetry groups can seed darkly charged ALPs. Illustrative examples of ultraviolet completions which result in darkly charged ALPs at low-energies are provided as well. The darkly-charged ALP scenario can be generalized by including dark gauge interactions. In this paper, we have considered only the case with no such interactions.

We construct the Carrollian limit of NS–NS and heterotic supergravity through an ultra-relativistic expansion of the fields. An appropriate scaling of the dilaton renders the measure finite and compensates the divergences arising from the NS-NS supergravity Lagrangian, giving a finite action as $w\rightarrow\infty$. We then extend the construction to heterotic supergravity (neglecting fermions) by incorporating the non-Abelian gauge field together with the Green–Schwarz (GS) mechanism. The resulting theory contains a finite gauge sector consistently coupled to gravity, and the GS mechanism for the Carrollian 1-form field can be trivialized imposing field redefinitions. Then, we investigate the Carrollian equations of motion by both expanding the relativistic equations and deriving them from a variational principle. We also show that the leading $\alpha'$-corrected $\hat{\rm Riem}^2$ contribution remains finite under a rescaling of the string parameter $\alpha'\rightarrow \frac{\alpha'_c}{w^2}$, opening further research towards the full four-derivative effective action. Finally, we discuss the potential connection with the worldsheet formalism of the Carrollian string theory.

In AdS/CFT, one often finds claims along the lines that “spacetime emerges from entanglement." This paper argues that behind these general statements hide three distinct emergence claims about, respectively, metric, gravitational dynamics, and topological connectivity. Thus, despite being advertised with the same terminology, these results are not about the same spatiotemporal aspects. They can therefore not just be grouped as evidence for one unanimous conclusion, though they do point in similar directions. The paper also investigates whether the three emergence claims satisfy two of the necessary conditions for emergence: Determination and novelty. The paper argues that none of the emergence claims satisfies the determination condition: More than entanglement is needed to furnish the emergence basis. Besides entanglement, the emergence basis for the bulk metric must include the induced metric on the boundary. Thus, this claim might not satisfy the novelty condition for emergence that the emergent should be novel as compared to the emergence basis. Likewise, the emergence basis for topological connectivity seems to include connectivity whereby this emergence claim is also questionable. The paper concludes that only gravitational dynamics is novel compared to the fully furnished emergence basis.

We investigate Unruh-DeWitt detectors coupled to composite observables of a quantum scalar field, including quadratic coupling to the field momentum and coupling to the local energy density. We develop a distributional framework for evaluating the corresponding detector response functions and apply it to detectors crossing the Rindler firewall. While we recover the finite response of the derivative-coupling model, we show that quadratic momentum coupling leads to products of distributions that do not admit a canonical, regulator-independent definition in the sharp-firewall idealization. The vacuum correspondence between the local energy-density and quadratic momentum responses motivates the conjecture that analogous difficulties may arise for energy-density coupling in the sharp firewall model. Within the sharp, pointlike composite-coupling model considered here, our analysis further suggests that these pathologies originate from the discontinuous severing of correlations across the Rindler horizon.