Papers

The flavor diagonal CP violation of elementary particle physics contributes to the atomic, nuclear, and nucleon electric dipole moments (EDMs), T-violating neutron optics, and to the angular correlations of beta decay. In this contribution, we review the basics and the importance of CP violation in the search for new physics beyond the standard model, the recent progress in the quantification of the hadron level CP violation contributing to the aforementioned observables, and finally the current attempt to solve the strong CP problem without additional interactions and fields.

In light of recent cosmological observations, we examine a generalized Chaplygin gas model with a redshift-dependent exponent as a framework for describing the dark energy and dark matter content of the Universe. Specifically, we treat this fluid as a single unified component and test it against late-time background observational data. We employ Type Ia supernova data, cosmic chronometers, and baryon acoustic oscillations from the second data release of the Dark Energy Spectroscopic Instrument. We perform a Bayesian analysis for parameter estimation and compare the model with $\Lambda$CDM. We find that the generalized Chaplygin gas provides systematically higher values of the combined likelihood; nevertheless, once the larger number of free parameters is taken into account, both the Bayesian evidence and the Akaike Information Criterion suggest that the model is statistically indistinguishable from $\Lambda$CDM.

We study the quantum dynamics of the dynamical region of the Reissner–Nordström geometry using a minisuperspace reduction and affine quantization, which is naturally suited for positive-definite geometrical variables. The resulting Wheeler–DeWitt equation becomes separable, yielding Hermite-polynomial modes in one sector and Gaussian-like radial solutions in the other. Affine quantization introduces additional short-distance contributions that modify the small-radius behaviour of the wave function. By constructing normalizable semiclassical wave packets, we analyze the resulting probability distributions in minisuperspace and the role played by the electric charge in the quantum dynamics. Our results extend previous affine-quantization studies of the Schwarzschild case to the charged Reissner–Nordström geometry.

In the context of pertubative aspects of Lorentz-violating theories, we study the divergent one-loop two-point functions of a Lorentz-violating (LV) extension of scalar QED containing a dimension-five CPT-odd nonminimal coupling. The model is defined through a generalized covariant derivative involving a constant background vector and the dual electromagnetic field strength. After expanding the action, we derive the full set of vertices relevant for the photon and scalar self-energies, including the mixed minimal-nonminimal seagull interaction diagram required by the gauge invariance. Using dimensional regularization, we compute the divergent parts of the vacuum polarization and scalar self-energy. The complete photon two-point function is shown to be transverse since the mass-dependent pieces generated by the mixed and purely nonminimal bubble graphs cancel against the corresponding seagull graphs, leaving higher-derivative CPT-odd and CPT-even LV gauge counterterms. The scalar self-energy generates LV kinetic and higher-derivative counterterms. The calculation confirms that gauge invariance is preserved, while the nonminimal interaction should be understood within an effective-field-theory expansion.

We study the role of Weyl symmetry breaking in conformal gravity and the residual scale symmetry of Einstein gravity. The corresponding action is characterized by a dimensionless coupling $\alpha$, determined by the ratio between the de Sitter and Planck scales. We show that this quantity admits a natural interpretation as the Bekenstein-Hawking entropy of de Sitter spacetime. Combining ideas from the functional renormalization group, holography, and emergent gravity, we propose a microscopic interpretation of $\alpha$ as a measure of the degrees of freedom associated with the de Sitter horizon. In this framework, the renormalization group flow of $\alpha(k)$ encodes the scale dependence of these microscopic degrees of freedom. Requiring this flow to be monotonically increasing toward the infrared leads to a cosmological constant of the same order as the observed one, suggesting an entropic solution to the old cosmological constant problem. This remarkably small value can therefore be understood as a direct consequence of the extraordinarily large number of degrees of freedom in our de Sitter universe.

Warm inflation perturbations are sourced by both thermal and quantum fluctuations and are commonly computed through stochastic realizations of the perturbation equations, as implemented in the publicly available code SWIM. Deterministic formulations based on correlation matrix evolution provide a computationally efficient alternative, but can become numerically ill-conditioned when the perturbation variables evolve over widely different scales. In this work, we extend SWIM by introducing a deterministic module, DSWIM, based on correlation matrix evolution. We introduce a physically motivated scaling matrix transformation derived from the effective Hubble scaling of the perturbation variables. The transformed system preserves the primordial curvature power spectrum exactly while substantially improving the numerical conditioning of the deterministic evolution equations. Using representative warm inflation models, we show that the scaled framework suppresses numerical artifacts, improves the robustness of the deterministic evolution, and yields substantial computational speedups while preserving accuracy. We further show that correlated thermal noise contributions arise naturally through the diffusion matrix structure, resolving previously observed discrepancies between stochastic and deterministic implementations. Our results establish DSWIM as a numerically robust and computationally efficient framework for computing warm inflation scalar perturbations.

The dynamics of a massive scalar field non-minimally coupled to gravity in an expanding de Sitter universe are investigated. It is shown that a comoving observer identifies the Bunch–Davies state as the vacuum, whereas a static observer perceives the same state as a thermal bath at the Gibbons–Hawking temperature. Motivated by this observer dependence, a thermal formulation based on Thermo Field Dynamics is developed by combining the geometric doubling associated with the cosmological horizon with the statistical doubling induced by a intrinsec thermal bath. The resulting construction reveals that the doubling procedure is not merely a mathematical artifact, but rather a manifestation of the global causal structure of spacetime together with finite-temperature effects. The temporal evolution of the Bogoliubov angle is analyzed and the corresponding particle number densities are evaluated in both comoving and static frames. In the radiation limit, the comoving number density remains conserved, providing a thermodynamic evolution consistent with that of the Cosmic Microwave Background, whereas in the static frame finite-temperature effects sti\-mulate Parker particle creation. For massive and non-minimally coupled fields, the interplay between geometric and statistical temperatures gives rise to a characteristic thermal scale and a nontrivial dependence on the initial conditions. These results provide a unified framework for describing quantum fields in de Sitter spacetime in the presence of both apparent horizon-induced and intrinsec thermal effects.

We compute the next-to-leading order (NLO) angular impulse (spin kick) in the scattering of Kerr black holes using the Kosower–Maybee–O'Connell (KMOC) formalism. Our approach is based on on-shell scattering amplitudes and leading singularities, allowing for a direct extraction of classical observables from quantum amplitudes. We derive compact expressions for the spin-dependent angular impulse valid to all orders in the spin variables at the integrand level, and show that these results reduce to known expressions in the appropriate limits. We perform detailed consistency checks: the conservative result preserves both the covariant spin supplementary condition and the spin magnitude through 2PM order, and the quadratic-in-spin conservative result agrees with existing radial-action results after translating between the direct KMOC spin kick and the radial-action observable. In addition, we extract the corresponding non-relativistic gravitational potential from the triangle leading singularities, obtaining a representation that resums spin effects and reproduces the known spin-orbit interaction at linear order. Our results provide further evidence for the efficiency of amplitude-based methods in classical gravitational dynamics, and highlight the KMOC formalism as a powerful framework for computing spin-dependent observables in binary black hole scattering.

The gravitational-wave induced freeze-in of Maleknejad and Kopp (2026) produces dark fermions from a stochastic gravitational-wave background, but requires them to acquire mass by separate means. We develop the Quadratic Spinor Lagrangian (QSL) formulation of general relativity, extended to Einstein–Cartan, as a framework that supplies this mass geometrically. The spinor 1-form built from a single Dirac field is purely spin-1/2 – its gamma-traceless (spin-3/2) part vanishes identically – so the propagating excitation is a Dirac fermion, the same content as the produced Weyl fermion. A cosmological spinor condensate sources a vectorial trace torsion $K\propto\dot\chi/\chi$, and an explicit Clifford reduction shows that this torsion gives the fermion a pure Dirac mass $M_{eff}=(1/\sqrt6)\,|\dot\chi/\chi|$, with no pseudoscalar or cross terms. The mass is not a free parameter but is locked to the Hubble rate at production, $M_{eff}\simeq(c_\chi/\sqrt6)H_*$, making the relic abundance a function of essentially the single scale $H_*$ ($\Omega h^2\propto H_*^{5/2}$) and supplying the mass the parent mechanism must postulate. Whether promoting the spinor 1-form to an independent field yields a propagating spin-3/2 candidate is a distinct dynamical question; Paper II shows that it does not – the QSL channels all propagation into the gravitational sector – so the composite spin-1/2 Dirac fermion is the unique QSL dark-matter candidate. We discuss the resulting dark-matter phenomenology and its link to asymptotically free scalar-field cosmology.

The gravitational production of dark matter from stochastic gravitational waves requires the produced fermion to acquire a mass by unspecified late-time physics. We show that this mass is supplied by spacetime torsion alone – no Higgs sector and no free mass parameter. In the Quadratic Spinor Lagrangian formulation of general relativity, extended to Einstein–Cartan, a cosmological spinor condensate generates a vectorial trace torsion $K\propto\dot\chi/\chi$; an explicit Clifford reduction confers on the produced spin-1/2 fermion a pure Dirac mass $M_{\rm eff}=(1/\sqrt6)\,|\dot\chi/\chi|$, with no pseudoscalar or cross terms, locked to the Hubble rate at production, $M_{\rm eff}\simeq(c_\chi/\sqrt6)H_*$. The relic abundance is then a one-parameter prediction, $\Omega h^2\propto H_*^{5/2}$, and the spin is fixed: the same framework admits no propagating spin-3/2 mode, so the composite spin-1/2 Dirac fermion is its unique dark-matter candidate.

We investigate nonlinear electrodynamic effective field theories (EFTs) through the relative entropy evaluated in suitable background electromagnetic fields. In this setup, the relative entropy encodes information about the infinite tower of higher-dimensional operators and provides a systematic probe of nonlinear EFT effects. We study these features in fermionic QED, scalar QED, and Dirac-Born-Infeld theory using perturbative analyses, resummation techniques such as Borel–Laplace resummation, and non-perturbative approaches including the Schwinger proper-time method. In the weak-coupling regime, we show that the non-negativity of the perturbative relative entropy imposes sign constraints on finite truncations of higher-dimensional operators, generalizing familiar positivity bounds on leading EFT coefficients. We further show that violations of non-negativity in the strong-coupling regime admit qualitatively different interpretations depending on the framework: perturbatively analyzed violations diagnose the breakdown of the truncated EFT expansion, whereas violations in resummed or genuinely non-perturbative relative entropy signal physical instabilities of the system, such as the Schwinger effect. Extending the analysis to broader classes of UV completions, including theories with factorial or power-law growth of EFT coefficients, we derive general constraints on nonlinear electrodynamic EFT effects from the non-negativity of the resummed relative entropy. Our results suggest that relative entropy provides a unified diagnostic of perturbative consistency and non-perturbative stability in nonlinear EFTs.

The composite Quadratic Spinor Lagrangian (QSL) propagates a spin-1/2 Dirac fermion whose mass is generated geometrically by cosmological trace torsion. It is natural to ask whether promoting the spinor 1-form $\Psi_\mu$ to an independent Dirac-vector field yields a genuine spin-3/2 dark-matter candidate. We prove that it does not. Three results combine into a no-go theorem. First, the torsional term, computed exactly by Clifford reduction, is a frame-aligned mass confined to the time-component sector – not a uniform spin-3/2 mass. Second, the second-order form $2 D\Psi \gamma_5 D\Psi$ has identically vanishing kinetic and cross terms for the independent field: as a component expression it is the boundary part of the spinor-curvature identity and carries no bulk dynamics. Third, the genuine dynamics therefore reside in the curvature side of that identity, $S=-\int\bar\psi\psi R\sqrt{-g}$, in which the metric $g=\Psi\otimes_S\Psi$ and the scalar $\bar\psi\psi$ are both composites of $\Psi$; the second variation consequently factors, $\delta^2S=\mathcal Q(h_{\mu\nu}[\delta\Psi],\delta\Phi[\delta\Psi])$, through the linearized metric and a scalar, both massless. Every propagating pole therefore lies on the metric light cone $k^2=0$ – the graviton and a scalar – and no massive spin-3/2 mode exists, on any background. This is the dynamical completion of the kinematic fact that the composite spinor 1-form has no spin-3/2 part, and it establishes the composite spin-1/2 Dirac fermion as the unique propagating matter excitation, and the unique dark-matter candidate, of the QSL. Through the super-SL(2,C) structure this surviving mode is naturally read as the Goldstino of the local supersymmetry broken by the metric condensate – a composite, gravitational descendant of the light-gravitino dark matter of Fayet and of Pagels and Primack.

In this paper, using the example of a two-dimensional nonlinear sigma model with the Heisenberg group, we compare two variants of chiral field decomposition into a background part and a fluctuation. It is shown that only one of these methods is consistent with the construction of the generating functional by introducing a background field. Furthermore, we perform a one-loop renormalization of the quantum action, calculate power-law singularities in the two-loop approximation, and consider transition to an extended classical action. Finally, we study the consistency of the cutoff with special functional relations within the framework of the background field method.

In this article, we define and study the statistical physics of planar Carrollian systems. While it has been shown recently that, for general dimensions, the Carroll limit of Poincaré statistical physics typically does not converge, we show that thanks to the central extensions of the Carroll algebra in the plane, and by considering systems with angular momentum, there exists a well defined notion of planar Carrollian statistical physics. Using Souriau's geometric thermodynamics, we compute the partition function for particles on a uniformly rotating disc, and show that rotation is inevitable for thermal equilibrium of planar Carroll systems, with one of the central charges determining the direction of rotation. We derive thermodynamic quantities in particular entropy, which scales logarithmically with the disc area, and pressure, which follows the two-dimensional ideal gas law. Though all results are obtained from symmetry considerations, we also derive the corresponding effective Hamiltonian.

Cross-correlation searches for gravitational-wave backgrounds depend on the geometrical configuration (physical separation and relative orientation) of the detectors comprising the network. Applying standard techniques to a few simple examples, we illustrate how the relative orientation of a pair of Earth-based L-shaped laser interferometers can drastically impact the detectability of both isotropic and anisotropic gravitational-wave backgrounds.

We propose an orbital-angular-momentum-resolved extension of small-$x$ gluon tomography in hard diffractive dijet deep inelastic scattering. In the standard plane-wave setup, the elliptic correlation between the dijet relative momentum and the target recoil probes the elliptic component of the small-$x$ gluon Wigner distribution through a fixed transverse readout. We show that replacing the plane-wave lepton current by a twisted wave-packet current promotes this readout into a tunable OAM–Bessel projection kernel. The exchanged virtual photon is not treated as an asymptotic vortex particle; the OAM dependence enters through the transverse structure of the lepton electromagnetic current. The resulting observable is a family of $M$-resolved elliptic correlations $A_2^{(M)}(q_T,R_\gamma)$, where $q_T$ denotes the transverse Bessel scale of the projection kernel, not the transverse momentum of the exchanged photon. We derive the normalized linear response and show that it contains a subtraction from the deformation of the total diffractive rate. Consequently, the elliptic response can vanish while the diffractive rate remains finite. This finite-rate null is a normalized projection zero of the response to the target elliptic gluon component, not a disappearance of diffraction. It is not available as a tunable mode zero in the standard single plane-wave readout, and provides an external projection basis in which the response to the same small-$x$ elliptic geometry can be probed with either sign or tuned to zero.

An outstanding problem in the framework of conformal thermodynamics concerns the interpretation of variations in the central charge $C$. In this paper, we construct a novel central-charge Rényi entropy via the Casini-Huerta-Myers (CHM) map by considering thermal CFTs on a hyperbolic cylinder within a fixed charge, field theory volume and central charge potential $(\tilde{Q},\mathcal{V},\mu_C)$ grand canonical ensemble. We demonstrate that the resulting entropy satisfies all four fundamental Rényi entropy inequalities throughout the admissible range of $\mu_C$, establishing its consistency as a genuine Rényi measure. Physically, this novel measure extends conventional Rényi entropy by capturing the degree of entanglement across a statistical ensemble of holographic CFTs with fluctuating degrees of freedom. Furthermore, our conformal thermodynamic analysis of near-extremal configurations reveals that residual entropy arises from the central charge sector rather than thermal excitations. The mass gap that separates the extremal state and the first thermal excitation introduces a characteristic temperature scale $\tilde{T}_*$, which translates via the CHM map into a distinguished characteristic Rényi index $n_*$. Crucially, we propose that $n_*$ separates the theory space into two qualitatively distinct statistical regimes: a dominant-theory regime ($n > n_*$) governed by the most probable CFT realizations, and a multi-theory regime ($n < n_*$) where a broader spectrum of fluctuating theories and higher-energy modular excitations becomes increasingly relevant.

The conformal boundary condition for gravity fixes the boundary conformal class and the mean curvature, leaving the trace-free extrinsic curvature free as the conjugate response. It is the boundary-value form of York's conformal decomposition of gravitational data, shown to be well posed for Einstein metrics by Anderson. Witten identified it as the elliptic replacement for the ill-posed Dirichlet condition in the finite-boundary perturbative Euclidean gravitational path integral. We show that this perturbative construction admits no half-supersymmetric extension in linearized minimal supergravity. For fixed conformal bosonic data, no half-dimensional gravitino boundary condition (local or pseudodifferential, APS-type included, with any compatible ghost condition at highest-derivative order) closes the full preserved chiral supersymmetry. Supersymmetry first selects the natural local chiral gravitino datum. Acting back on this datum then produces the trace-free extrinsic curvature, precisely the response that the conformal prescription leaves unfixed. The obstruction is therefore not the failure of a particular elliptic ansatz: even the chiral/Robin completion that is LS-elliptic and BRST-compatible at highest-derivative order would impose Dirichlet control on a Neumann response. The obstruction is pointwise in tangential momentum and survives compensating gauge transformations. It is a linearized, highest-derivative obstruction, not a global or nonlinear no-go; nonlinear supercovariant boundary terms may evade it by tying the trace-free extrinsic curvature to gravitino bilinears.

Formulating a consistent integration measure for quantum geometric fluctuations without violating diffeomorphism invariance remains a theoretical challenge. In this work, a framework rooted in the statistics of discrete Poisson point processes is proposed. The formulation yields a double-exponential probability functional characterized by a capacity limit, which acts as an amplitude regularizer suppressing ultraviolet singularities. To evaluate this model at macroscopic scales, a statistical bifurcation of the stochastic action is identified. First, the macroscopic mean condenses to define the classical continuous spacetime background and its matter distribution. Second, at macroscopic scales, the Law of Large Numbers dictates that the residual ultraviolet noise maps into an infrared continuous zero-mean Gaussian martingale within the bulk. Third, this zero-mean Gaussian noise linearly generates standard quantum kinematic effects. Fourth, evaluating the non-linear exponential action separates the variance of this Gaussian noise from the linear cancellation, rectifying it into a macroscopic drift that manifests as the dark energy density. Diluted by the Bekenstein-Hawking entropy of the observable universe, this bulk variance dictates a continuous field cutoff at 6 TeV. Building upon this framework, broad phenomenological applications are demonstrated: (1) establishing a UV-finite effective field theory preserving gauge symmetries in 4D; (2) constructing a topological model of particles deriving Standard Model hierarchies; (3) formulating a non-singular cosmological model predicting observed large-scale power suppression in the cosmic microwave background; and (4) deriving foundational axioms of quantum mechanics as emergent statistical phenomenologies. Collectively, this framework provides a falsifiable synthesis bridging discrete quantum geometry and continuous macroscopic physics.

We study the broken-symmetry phase of the Lipkin-Meshkov-Glick (LMG) model, whose two lowest states form a near-degenerate parity doublet split by tunnelling. We show that the same instanton action S_inst that sets the doublet splitting also controls how much parity information a static J_z magnetisation readout can extract. Although J_z measures magnetisation rather than parity - and so distinguishes the two wells easily while remaining almost blind to their relative sign - WKB barrier arguments together with exact diagonalisation show that the spectral gap, the total-variation distance, and the nonlinear distinguishability measures (Jensen-Shannon divergence and Chernoff information) share a single instanton exponent, rather than the doubled exponent a naive small-deviation expansion in the lobes would suggest. Exact diagonalisation up to N = 4500 supports a common leading exponent for all four quantities, with fitted values within a few percent of the WKB instanton value in the largest reliable windows. The same coupling acts strongly inside the doublet: its off-diagonal element grows as |J_01| -> N m_*/2, so the bath can disturb the parity label far more strongly than it can read it from a frozen histogram. We call this separation the static parity horizon - a benchmark for the idealised static J_z channel, not a universal bound on time-resolved monitoring. Restoring the full monitored dynamics, continuous-monitoring simulations (1.48 million full-LMG trajectories with matched QND controls across 77 independent settings) show that a time-resolved homodyne record extracts parity information hidden from the single-shot histogram, over a finite window of system sizes organised by the ratio xi = omega_01/Gamma_01 of coherent doublet rotation to measurement-induced dephasing, and closing again under strong measurement.

We analyze the effects of the magnetic field on the quark and gluon propagators within the functional QCD framework. By solving the coupled Dyson-Schwinger equations for the quark and gluon propagators, we find that the quark mass is generally enhanced in the presence of a magnetic field, leading to magnetic catalysis of the chiral condensate. Meanwhile, the magnetic field also induces an increase in the gluon screening mass. The enhancement of the gluon screening mass suppresses the quark-gluon interaction and thereby weakens the strength of dynamical chiral symmetry breaking, establishing a competing mechanism against magnetic catalysis. In particular, this enhancement of the gluon screening mass becomes dominant near the chiral phase transition, which in turn gives rise to inverse magnetic catalysis.

We present a numerical implementation of dissipative relativistic magnetohydrodynamics based on Bemfica-Disconzi-Noronha-Kovtun (BDNK) theory, in which first-order corrections render the equations causal without introducing additional dynamical variables. We show how these corrections can be incorporated in a finite-volume scheme describing the coupled dissipation of energy, momentum, and magnetic field, with the latter treated as a one-form charge. While a minimal set of BDNK terms can convert diffusive equations into telegrapher-type equations, we find that in the ultra-relativistic limit an additional correction is required for the system to behave in a stable and causal manner. With this set of equations, we develop an efficient method for primitive-variable recovery and validate the implementation through an analytical benchmark and various two-dimensional simulations.

We show that an oscillon can be understood as a localized discrete resonant (non-normalizable) mode. Specifically, oscillon in the vacuum arises from the threshold mode, which because of nonlinearity gets localized. Following this idea, we find wobblerons - nonlinear excitations of kinks, that is, oscillons-kink bound state. Now, the oscillon can also originate in an antibound mode, i.e., a discrete, positive energy but non-normalizable mode.

It was recently found that the quasinormal modes (or Ruelle–Pollicott resonances) of the SYK model at infinite temperature form a Christmas tree shape, reminiscent of AdS black holes. We generalise this computation to finite temperature, allowing us to continuously connect the infinite temperature results to the low temperature regime dual to JT gravity. We contrast the movement of the quasinormal modes with a few examples: various AdS black holes, dynamical phase transitions, and the large $p$ SYK chain. We find that the relaxation rate increases monotonically with temperature only at strong coupling, corresponding to the gravitational regime. Byproducts of our investigations are new results on operator growth that may be of independent interest.

We formulate four-dimensional finite-proper-time QED from a gauge-covariant source functional with a retained spectral lower boundary $s_0=\Lambda^{-2}>0$ and finite physical duration $\mathcal T$. Physically, the basic $s_0$ operation is a truncated Laplace transform: the arbitrarily small-proper-time part of the spectral integral, which carries the ultraviolet singularity, is excluded without imposing a cutoff on momentum space, while finite $\mathcal T$ expresses that a physical observable is prepared and detected during a finite experiment rather than by an infinite-time measurement. The retained $s_0$ belongs to the defining source construction and controls the correlated finite corrections after mass and charge matching. The charged interval and circle sectors are generated by the same covariant heat semigroup, while the photon covariance carries the same retained lower bound at the source level. At every fixed perturbative order, gauge covariance gives the Ward–Takahashi hierarchy and an assembled graph-level quadratic-form bound establishes ultraviolet finiteness. The physical electron, positron, and transverse-photon poles retain their canonical residues, and the fixed-order cutting relation uses the matched daughter domains on the stated regulated continuation domain. Mass and charge renormalisation are replaced by finite matching, while independent observables retain correlated $s_0$ dependence. At fixed $s_0>0$, the Euclidean source has a nonperturbative definition. Its physical standing-wave response is obtained order by order from the continued FPT amplitudes with the same finite-duration channel data. An exact all-coupling physical boundary realisation requires additional channel-norm control. The limits $s_0\to0^+$, $\mathcal T\to\infty$, and exact all-coupling free-space exhaustion are separate limiting questions and are not used to define the theory.

We give the complete solution of the one-parameter deformation of the six-vertex model on dynamical lattice introduced in [1] and dubbed gravitational seven-vertex model. The statistical model in question is mapped to a gas of self- and mutually avoiding loops on dynamical triangulations, with a temperature coupling controlling the volume not occupied by loops. The phase diagram is characterised by massive, dilute and dense critical phases, similarly to the gravitational O(n) loop model. There is however an important difference – in our model the weights of the loops are not topological but depend on the form of the loop and on the curvature defects of the lattice via lattice spin connection. The seven-vertex model on dynamical lattice is nevertheless exactly solvable after being reformulated as a large-N matrix model, which we will refer to as 7vMM, and the solution in the scaling limit was found in [1]. Here we derive the full solution in terms of Jacobi theta functions and present the (non-algebraic) spectral curve of 7vMM in a parametric form. We obtain the phase diagram in the space of the two coupling constants – the cosmological constant and the temperature – and identify the critical phases along the boundary of the physical domain. We derive the scaling solution of [1] as the asymptotic of the full solution in the vicinity of the tricritical point separating the phases of dense and massive loops.

In this work, we study a $\mathbb{Z}_3$-symmetric extension of the Standard Model with three hyperchargeless $SU(2)_L$ fermion triplets responsible for neutrino mass generation $\textit{via}$ the Type-III seesaw mechanism together with a complex scalar singlet $\chi$ whose vacuum expectation value spontaneously breaks the $\mathbb{Z}_3$ symmetry. Radiative corrections induced by the Yukawa interactions between the $SU(2)_L$ fermion triplets and the complex scalar singlet $\chi$ generate a Coleman-Weinberg vacuum bias that lifts the degeneracy among the $\mathbb{Z}_3$ vacua, leading to the annihilation of unstable domain-walls. Consequently, the degeneracy among the $\mathbb{Z}_3$ vacua is lifted radiatively through the Coleman-Weinberg effective potential, generating a dynamical bias term that triggers the annihilation of unstable domain walls. We perform a numerical analysis consistent with current neutrino oscillation data and identify viable regions of parameter space accommodating the observed neutrino masses and leptonic mixing parameters. The observed baryon asymmetry of the Universe is generated through thermal leptogenesis $\textit{via}$ the out-of-equilibrium decay of the lightest fermion triplet for masses around $\mathcal{O}(10^{9})\,\mathrm{GeV}$, consistent with the Type-III seesaw framework. Depending on the choice of model parameters, the predicted gravitational-wave spectrum can fall within the sensitivity reach of future space-based and ground-based gravitational-wave detectors. Our framework therefore establishes a correlation between neutrino mass generation, leptogenesis, radiative domain-wall instability, and gravitational-wave phenomenology.

A holographic code assigns a state-dependent entropy remainder to every boundary region, but such remainders need not be the extremal lengths of any one bulk metric. We study this common-source question for the proto-area of a calibrated recovery, the entropy of a boundary region minus that of the matter recovered from it. At zeroth order the reference values must match the lengths of one reference geometry in a fixed renormalization scheme, and this matching also determines the entropy-to-length factor. On a graph with a fixed minimum-cut chamber the data derivatives must lie in the image of the cut-incidence matrix, whose left null vectors are witnesses. On the hyperbolic disk the first variation of renormalized length is the rank-two geodesic X-ray transform, with closed range in an adapted data space, and the geodesic displacement, fixed by a forced Jacobi equation, enters at second order. The resulting normal Hessian gives a gauge-invariant criterion, necessary and sufficient, for a regular pair of response coefficients to come from one metric two-jet. For the constant-curvature family generated by a boundary reparametrization the Hessian has a nonzero rank-four mode, so the image of the length map is curved. For a fixed recovery the proto-area Hessian is minus the Bogoliubov-Kubo-Mori information lost in recovery, which the Petz map decomposes orthogonally at a product reference, and which, on a finite-dimensional space of logical directions with positive minimum retained fraction, is at most a sharp multiple of the retained information. Geometric realization requires this loss to reproduce the normal length Hessian on every interval. Two codes show that exact regional area operators can fail to sew into one graph geometry, and that a matched reference with vanishing first response can fail at second order. All criteria refer to one recovery branch and one extremal-surface branch.

We study collisions of domain walls in $SU(N)$ gauge theories using the Polyakov-loop effective potential models. We find that string junctions play a crucial role in the dynamics of $Z_N$ domain walls. In $SU(3)$ gauge theory, the merger of two non-planar $Z_3$ domain walls into a single wall proceeds via the creation of a vortex–antivortex pair in $2+1$ dimensions. In $SU(4)$ gauge theory, low-energy collisions of $Z_4$ walls result in the formation of a single domain wall without the creation of vortices. At higher collision energies, two $Z_4$ domain walls can either bounce back or scatter into another pair of domain walls through the formation of vortices. The creation of vortex–antivortex pairs generalises to the creation of string loops in $3+1$ dimensions for both gauge theories. These results demonstrate a direct dynamical role for topological strings in the evolution of center-domain-wall networks and reveal a new aspect of defect dynamics in non-Abelian gauge theories.

We construct exact timelike junctions between compact flat cavities and a Kinnersley photon-rocket exterior. The shells satisfy the strict surface dominant energy condition and steer subluminally under nonnegative radiation. Burns joined at static spheres give $m_f/m_i=e^{-3L}$ for exterior velocity-space path length $L$; the supported cavity center obeys a separate sharp bound. Self-similar shells require anisotropic stress and have growing normal modes with the ambient geometry and coefficients held fixed. A separate elastic model admits local self-gravitating recoil control with outward emission. At zero gravitational coupling, exact unstrained turns yield sharp fuel bounds and travel limits at fixed duration. Limits on angular concentration and inward emission reduce efficiency. For smooth emission and positive inner-face density, stress-free recoil requires photons to enter the cavity. Self-gravitating settling after a turn remains open.