Papers

Quiver-invariant dualities relate distinct 4d N=1 supersymmetric gauge theories that arise as worldvolume theories on a D3-brane probing the same toric Calabi-Yau 3-fold. These dual theories share an identical quiver and differ only in their superpotentials. We show that quiver-invariant dualities are realized by tilting mutations on the brane tilings that realize these theories. Among the 42 toric phases of the H1121 model, we identify three general families of tilting mutations, all characterized by the reversal of the orientations of zig-zag paths within the mutation region of the brane tiling. We present new examples of quiver-invariant dualities, given by five doublets and one triplet of toric phases with identical quivers, for which we verify that the brane tilings related by the tilting mutations correspond to the same toric Calabi-Yau 3-fold H1121.

The recent observation by the LHCb Collaboration of a new beauty–strange meson $B_{s0}^*(5700)^0$~\cite{LHCb:2026Bs0star}, under the conditional assignment $J^P=0^+$ provides an important new test of the chiral organization of heavy-light hadrons. More than three decades ago it was proposed that the coexistence of heavy-quark spin symmetry and spontaneously broken chiral symmetry implies that every heavy-light spin multiplet should possess an opposite-parity partner separated by a nearly universal mass gap determined primarily by the dynamics of the light degrees of freedom~\cite{Nowak:1993vc,Bardeen:1993ae}. This chiral doubling scenario was later developed into a quantitative heavy-hadron effective theory and extended to the complete charm and beauty spectra. In particular, the strange beauty sector was predicted to exhibit a parity splitting closely related to that of the strange charm sector, with only small $1/m_Q$ corrections. We briefly review the symmetry origin of chiral doubling, derive the universal parity splitting through the heavy-hadron chiral effective theory, and discuss the new LHCb observation in the context of the original theoretical predictions. Taken together with the established charm spectrum, if the new beauty-strange state is confirmed to have $J^P=0^+$, its mass is consistent with its interpretation as the chiral partner of the ground state $B_s^0$. Finally, we stress that the above confirmation of the spin and parity imposes in the chiral doubling scenario an existence of yet unobserved, very narrow beauty-strange meson with assignment $1^+$ at 5747 $\pm$ 2 MeV. This work is dedicated to the memory of our friend and collaborator Mannque Rho (1936–2026).

We discuss the impact of tensor-induced backreaction at second order in perturbation theory on primordial black holes production in single-field inflationary models, where the comoving curvature power spectrum is amplified by a transient ultra-slow-roll phase. Although the leading perturbative correction is mostly negligible in standard slow-roll evolution, it becomes important in non-attractor regimes, going in the direction of limiting the suppression of the first slow-roll parameter $\varepsilon$ and reducing the enhancement of the scalar power spectrum. We then go beyond the standard perturbative analysis by considering the background parameters as effective quantities with evolution self consistently determined by a closed system of backreaction equations. This analysis, which leads to a partial resummation of the effect beyond the perturbative treatment, confirms the limitation of the suppression of $\varepsilon$ by consistently showing how the effect remains important even after accounting for the effective evolution of the background in the evaluation of the backreaction itself. Finally, we discuss how, taking into account the tensor-induced backreaction, the fine-tuning associated with the value of the peak amplitude of the scalar power spectrum is strongly reduced.

The leading asymptotic growth of Lanczos coefficients is controlled by spectral tails and furnishes a coarse classification of Krylov dynamics. We show that the global topology of the spectral measure, specifically the number of connected components, the gap structure, and the behaviour at gap-closing transitions, encodes a finer hierarchy of dynamical invariants invisible to tail-based arguments. Using the Riemann-Hilbert formulation of orthogonal polynomials and Deift-Zhou steepest descent, we recover the Freud growth laws $b_n\sim n^{1/\beta}$ for single-cut measures and determine their sub-leading corrections from endpoint data. Gapped spectra produce quasiperiodic Lanczos oscillations at a frequency fixed by the filling fraction of the spectral bands alone, and hence predictable from the band edges. We verify this in the SSH chain and its next-nearest-neighbour deformation. At a gap-closing transition the oscillation amplitude is governed by the Hastings-McLeod solution of Painlevé II, decaying as $n^{-1/3}$ at criticality and interpolating between the gapped and merged phases, so that the topology change of the spectral curve is realised as a Krylov phase transition. We also demonstrate that, while in the conformal limit of SYK the operator scaling dimension is invisible in the leading rate $\alpha = \pi T$, it can be extracted from the subleading offset $b_0 = \pi T(\Delta - \frac{1}{2})$. These results establish a refined notion of universality in operator growth, classified by spectral topology rather than spectral tails alone.

The quantum-mechanical two-sided Bogoliubov inequality provides upper and lower bounds for the free energy required to separate a system of interacting particles into independent subsystems. The bounds can be calculated straightforwardly from the ensemble average of the interface energy, bypassing the direct evaluation of the free energy. In this work, we generalize the two-sided Bogoliubov inequality to arbitrary von Neumann algebras by employing the Araki-Uhlmann relative entropy and the framework of unbounded perturbation theory of KMS states. Furthermore, we obtain variational expressions for the relative free energy that extend existing bounded-perturbation principles to the unbounded setting. Crucially, these mathematical developments yield a physically well-founded thermodynamic criterion for the quantification of entanglement in infinite-dimensional systems.

We investigate the semiclassical Hawking evaporation of a two-dimensional Callan-Giddings-Harvey-Strominger (CGHS) black hole perturbed by first-order Horndeski scalar-tensor couplings. By evaluating the exact scalar curvature invariants, we demonstrate that coordinate singularities near the apparent horizon parametrize a physical deformation of the surface gravity while preserving a strictly regular event horizon. In the linear-order $\gamma_3 \Phi X$ coupling sector, the surface gravity and correspondingly the Hawking temperature decreases dynamically as the black hole loses mass. Extrapolating this cooling effect via a resummed temperature equation suggests that evaporation halts, potentially leaving behind a stable, macroscopic cold remnant at the boundary of perturbative control. Utilizing both the conformal trace anomaly and the Robinson-Wilczek gravitational anomaly, we establish that the asymptotic radiation flux identically reflects this geometric shift. Consequently, the fine-grained entanglement entropy of the Hawking radiation departs from linear growth and transitions to an asymptotic logarithmic regime. This indicates that quantum information may be permanently retained within the remnant, altering the standard semiclassical Page curve without requiring a breakdown of horizon regularity.

In the context of quantum cosmology, we study quantum entanglement in solutions of the Wheeler–DeWitt equation for a homogeneous inflaton–gravity system coupled to perturbations. The wave function describing the homogeneous degrees of freedom is entangled with the wave function describing the perturbations, and this may lead to potentially observable effects on the inflationary spectra. We restrict our analysis to two simplified models that admit a future de Sitter attractor, while neglecting non-adiabatic effects and contributions of order $\mathcal{O}(\hbar^2)$ in the Mukhanov–Sasaki equation. Analytical expressions for the resulting spectra are obtained by marginalising over the homogeneous inflaton variable and can be evaluated in regimes where reliable approximations are available. Small deviations from the standard semiclassical spectra are indeed generated, and these are significantly larger than the quantum-gravitational corrections usually considered in this context.

We study the $U(1)^4$ charged black brane solution of four-dimensional gauged supergravity and analyze the fermionic response in this geometry, which is holographically dual to $3d$ $\mathcal{N}=2$ SCFT ABJM models. Similar to \cite{DeWolfe:2013fha}, we show that a gap exists in the states of the conformal field theory, which corresponds to the different limiting behaviors of the two unequal chemical potentials of the four-charge geometry. We study the behavior of this gap and also the stability of the near-horizon geometry by changing the parameters of the theory in various orders. We then categorize the $56$ fermion modes of the geometry, find the coefficients of the Dirac equations for each mode, and comment on the behavior of the solution of the Dirac equation in different near-horizon limits. We then uplift the geometry to five-dimensional and then to eleven-dimensional geometries and, similar to \cite{Fareghbal:2008dy}, we show that in both cases, a piece of $\mathrm{BTZ} \times \mathrm{S}^2$ or $\mathrm{AdS}^3 \times \mathbb{R}^2$ emerges, and as a result, a decoupling sector in the field theory exists. We study the singularity of the near-horizon $4d$ geometry and the mentioned gap in these uplifted geometries.

We demonstrate that a Bianchi-I spacetime in general relativity must be geodesically past-incomplete under the assumption of the null energy condition and provided there exists a time in which the universe is expanding in all directions. Spacetimes which are always contracting along at least one direction are not subject to the conclusion, and we provide an explicit example. A distinguishing feature of our theorem is that it makes no assumption on the global topology of the spacetime.

Genuine multi-entropy is the part of the $\mathtt{q}$-partite multi-entropy that captures entanglement genuinely shared among all $\mathtt{q}$ parties, rather than entanglement already present among fewer subsystems. It was recently proposed that this genuine part – so-called a multipartite entanglement signal – can be studied via the graph-encoded manifold (GEM) built from the underlying $\mathtt{q}$-partite multi-entropy permutation family: reading its $\mathtt{q}$-colored contraction graph $\Gamma_{\mathtt{q},n}$ as a triangulation by $(\mathtt{q}-1)$-simplices. Focusing on $\mathtt{q}=4$, we classify the topology of every vertex link of $\Gamma_{4,n}$ and find $\chi_{\rm link}(n)=n(3-n)$: the graph satisfies the GEM condition, namely every vertex link is a two-sphere, if and only if $n=2$, while for every $n\geq3$ the vertex links are closed surfaces of strictly positive genus $g_n=\tfrac12(n-1)(n-2)$, so that the graph instead defines a simplicial complex with a conical singularity at every vertex.

We construct a nonlinear electrodynamics (NLED) model for a static magnetic black hole. Rather than imposing a regular center, we require a Maxwell weak-field limit, finite magnetic self-energy, a positive and subluminal electromagnetic cone, the standard energy conditions, and a static exterior that satisfies known sufficient stability criteria. A positive mixture of power kernels restricts the exponent to $1/4<\gamma\leq1/2$. For the minimal two-kernel model, with $\gamma_1=1/3$ and $\gamma_2=1/2$, the field equations admit an exact solution in terms of incomplete beta functions. For the branches with nonnegative Schwarzschild mass parameter $M_0$, the metric function is strictly increasing, so there is at most one positive-radius horizon and no inner Cauchy horizon. We construct the maximal extension and show that the black-hole, horizonless, and critical branches have spacelike, timelike, and null singularities, respectively. The representative black-hole families have positive temperature and negative fixed-charge heat capacity. Electromagnetic waves split into ordinary and extraordinary optical branches. We calculate their photon spheres, shadow radii, instability rates, and illustrative Event Horizon Telescope size bands. We also construct ISCO-truncated thin-disk images. The full images remain close, but jointly normalized residual maps and radial profiles reveal a coherent branch-dependent shift near the lensed inner edge and the critical region. The extraordinary branch moves the critical curve outward and partly compensates the shadow reduction caused by magnetic charge.

Quantum field theories with ghosts can be unitary and perturbatively stable, yet the negative-norm states of their conserved indefinite inner product obstruct a probabilistic interpretation. This problem is especially relevant to renormalizable quantum gravity. The focus of this paper is the real-spectrum regime, in which the interacting Hamiltonian has an exact $\mathbb{Z}_2$ symmetry $Q$, called exact ghost parity. Its eigenvalue on each energy eigenstate equals the sign of the norm, and it reduces to free ghost parity at zero coupling. Imposing $Q$ as a superselection charge defines a new theory in which the physical states have definite ghost parity and the observables commute with $Q$. The native Born rule then yields non-negative probabilities, while the optical theorem acquires a direct probabilistic interpretation. The propagator decomposes into $Q$-sector spectral representations with fixed-sign spectral functions and no complex poles on the physical sheet. Finally, a similarity transformation yields a Hermitian perturbation theory that preserves free ghost parity order by order, making the exact superselection structure perturbatively manifest.

We present an exact analytical model of axisymmetric gravitational collapse leading to the formation of the Kerr black hole. The model depends only on the total mass ${\cal M}$ and a time dependent rotation parameter $a(v)$, and incorporates both the extremal Kerr black hole and a novel quasi extremal regime without requiring $a\approx{\cal M}$. The evolution develops curvature singularities induced by $a(v)$, which are expected to remain enclosed within a trapped region close to the evolving Kerr radius $r=h(v)$. It also predicts a transient anisotropic exterior curvature decaying as $1/r^2$, which may imprint observable signatures associated with the formation of a rotating black hole. The present construction should therefore be interpreted as an exact analytical description of the final stage of rotational gravitational collapse, immediately preceding the formation of the Kerr black hole.

We introduce a bootstrap method for three-dimensional conformal field theories based on product analytic functionals. The construction combines one-dimensional analytic functionals with dimensional reduction and provides an efficient alternative to the standard derivative basis. We benchmark the method in single correlator gap maximization problems for scalar and spin-two operators. At comparable basis size, the product functional basis gives stronger bounds and converges more rapidly, with the improvement becoming especially pronounced at large external dimension. Setting the external dimension to that of the three-dimensional Ising spin operator, we substantially sharpen the single correlator upper bound on the leading scalar dimension. We also sharpen the Nakayama-Ohtsuki necessary condition for critical points accessible by tuning a single parameter. In the spin-two problem, we find a new kink near $\Delta_\phi \simeq 4.16$, accompanied by a reorganization of the extremal spectrum. We also observe plateau structures at larger external dimension in both gap-maximization problems. Our results make product analytic functionals a promising tool for conformal gauge theories with heavy external operators and for probing the flat-space limit of holographic correlators; accessing both of these scenarios is challenging for conventional methods.

Dark matter and dark energy could be ultra-light pseudoscalar fields that couple to electromagnetism through a Chern-Simons term. This would cause a parity-breaking rotation of the plane of linearly polarized light from the cosmic microwave background, known as cosmic birefringence, which is not predicted by $\Lambda$CDM. Recent hints of a non-zero cosmic birefringence angle have been found in both the Planck Data Release 4 and ACT Data Release 6 datasets independently. This work jointly analyzes the polarized maps of both, leveraging the cross-power spectra between the two telescopes. Taking the reported instrumental priors at face value, the joint analysis yields $\beta = 0.277^{\circ} \pm 0.057^{\circ}$, which is non-zero with a statistical significance of $4.8\sigma$. A robustness test mitigating contamination from dust emission excludes $\beta = 0^{\circ}$ at $3.5\sigma$, and retrieving $\beta=0^{\circ}$ would require both the dust $EB$ modeling and instrumental priors to fail simultaneously. However, unresolved systematics in the data must be understood before we can draw strong cosmological conclusions.

We study semiclassical geometries induced by turning on identical sinusoidal scalar sources on two asymptotic anti-de Sitter (AdS) boundaries. Varying the source strength, we find that large and small wormhole solutions appear beyond a certain threshold. Above this threshold, the large wormhole is always the dominant saddle in the two-boundary gravitational path integral; there is no regime where wormholes are subdominant. Under the ensemble interpretation of the gravitational path integral, this implies that once wormhole solutions exist, the putative ensemble has exponentially large fluctuations relative to the mean. This is unlike previously studied examples of wormholes sourced by inhomogeneous matter which have a region in parameter space where wormholes are subdominant, and therefore the ensemble is sharply concentrated around the mean. Interpreting the bulk geometries as holographic renormalization group (RG) flows, we also find that the sinusoidal modulation of scalar boundary sources results in effective holographic $\beta$-functions which are multivalued, indicating exotic RG flows. In particular, disconnected geometries correspond to flows that return to the starting fixed point in the infrared, while wormholes describe flows to a gapped phase in the infrared.

Families of $\mathrm{Sp}(1)\simeq\mathrm{SU}(2)$ gauge theories with eight supercharges are found to have a Higgs branch which is an isolated symplectic singularity. These are, in some sense, the most “minimal” gauge theories as they only Higgs to a trivial theory. The matter content is $N$ fundamental half-hypermultiplets and one half-hypermultiplet in the $\mathrm{Sym}^k$ representation where $k=1,3,5,7$. The cases of $k=1,3$ reproduce the known Kraft–Procesi construction for minimal nilpotent orbit closures of $\mathrm{SO}(N+1)$ and the $g\mathrm{SO}(N)$ singularities of \cite{Bourget:2025wsp}, respectively. The cases $k=5,7$ are new isolated symplectic singularities which are termed $h\mathrm{SO}(N)$ and $i\mathrm{SO}(N)$, respectively. The classification of these isolated symplectic singularities is argued for through the Higgs mechanism, with Hilbert series and highest weight generating (HWG) functions computed for some cases. Each of the $g\mathrm{SO}(N)$, $h\mathrm{SO}(N)$, and $i\mathrm{SO}(N)$ families has a (quaternionic) one-dimensional member; these are the Klein $A_3$, $E_6$, and $E_8$ singularities, respectively. Our construction hence provides realisations of these Klein singularities as Higgs branches (hyper-Kähler quotients) of $\mathrm{Sp}(1)$ gauge theories, complementary to Kronheimer's construction \cite{Kronheimer:1989zs} using the $\widehat A_3$, $\widehat E_6$, and $\widehat E_8$ affine quivers. The Klein $E_7$ singularity is also realised as a Higgs branch (hyper-Kähler quotient) of an $\mathrm{Sp}(1)\times\mathrm{O}(1)$ gauge theory.

One-particle irreducible vertices encode renormalized interactions in quantum field theories, but their practical treatment remains challenging due to their high dimensionality and nontrivial dependence on external variables such as momenta or frequencies. We develop a functional framework that algebraically reorganizes the diagrammatic content of the vertex functions into more efficient building blocks and reveals several established vertex decompositions, such as parquet, single-boson exchange, asymptotic classes and symmetric estimators, as different realizations of a common functional structure. Based on Legendre transforms of the effective action of composite fields, the formalism shows that different vertex representations arise from different choices of composite degrees of freedom. We demonstrate that in our framework higher-order vertices can be systematically obtained via tree expansions, thereby extending the aforementioned decompositions beyond the four-point level. Because our findings are independent of any specific physical setting, the framework applies broadly to quantum field theories in condensed matter physics, particle physics, and beyond.

Neural network field theory (NN-FT) defines a field theory by a network architecture together with a probability density on its latent variables. For compact theories the local Gaussian sector is only part of the story: one must also sum over discrete topological sectors. We review a mixed continuous/discrete latent-variable construction and apply it to two compact bosons. For the Berezinskii–Kosterlitz–Thouless transition, a random Fourier feature spin-wave sampler supplemented by an explicit Coulomb gas vortex sector reproduces the Gaussian critical line below $T_c$, vortex proliferation above $T_c$, the essential singularity of the correlation length, and the Nelson–Kosterlitz jump. For the bosonic string, oscillator modes augmented by momentum–winding labels reproduce circle T-duality, Buscher transformations on constant toroidal backgrounds, self-dual current algebra enhancement, and a toy T-fold. The common lesson is that the same local neural sampler, paired with different discrete topological data, yields physically distinct compact theories. These proceedings are based on arXiv:2604.02313.

Rare fluctuations in physical systems depend on the detailed microphysics responsible for the fluctuations. In classical statistical systems, the large deviation principle has elucidated the role of semi-classics in describing this regime, and has simultaneously provided a the mathematical foundation of statistical mechanics. Large deviation theory for quantum system is considerably less developed. As all physical systems are fundamentally quantum mechanical, this leaves a major gap in our understanding of rare fluctuations relevant to statistical physics, cosmology, and more. In this paper, we develop the practical aspects of the theory of large deviations relevant for calculating rare events in physical systems from quantum walks to cosmology. We first analyze the case of the anharmonic oscillator coupled to a bath, showing explicitly how the system evolves from dominantly statistical (e.g. thermal) to quantum fluctuations. We then generalize these results, showing that the dominant rare fluctuations minimize the measurement-induced relative entropy. This perspective provides a thermodynamic description of a wide range of open quantum systems. We apply these results to random walks that arise in cosmology through stochastic inflation. We show that the evolution of the density matrix of long wavelength fields on a fixed de Sitter background breaks the KMS symmetry, giving rise to a stationary density matrix that does not respect detailed balance.

Field theories whose potentials have noninteger power laws $\alpha$ have found many applications, but are often claimed to have no lift to quantum field theory except as effective models. We define quantum lifts by expanding the classical potential in Hermite polynomials and then normal ordering at a mass scale shifted by a parameter $\beta$. We find that when $\alpha>2$, for sufficiently large $\beta$, the vacuum state can be perturbatively expanded in usual Fock states. We apply this to the following problem. The $\sigma=4$ Pöschl-Teller model has a $\phi^{5/2}$ potential. As the third derivative of the potential diverges in each vacuum, one expects the three point interactions to diverge in the vacuum. The model's kink has three shape modes and the least bound mode extends so far into the vacuum that its probability of being excited by radiation apparently diverges. We show that a deformation $\beta$ of order the meson mass or larger is sufficient to tame this divergence, although it nonetheless results in an excitation probability which is enhanced by a $\beta$-dependent fractional power of the inverse coupling.

We establish an integral basis for the B-brane central charges of certain Calabi-Yau fourfold flops and derive exact expressions for their monodromies using the grade restriction rule and window categories of the associated gauged linear sigma models. The monodromy is interpreted as an EZ twist associated with the contraction of an exceptional surface onto a curve of conifold singularities. We further illustrate a decomposition of the EZ twist into spherical twists for families of splitting configurations of the sixtic Calabi-Yau fourfold and a complete intersection in grassmannian.

We study holographic entanglement entropy in 3-dimensional AdS gravity with conformal boundary conditions which fix the conformal class of the boundary metric and its extrinsic curvature, $K$, while leaving the Weyl mode dynamical. Extending Lewkowycz-Maldacena-Dong's replica construction, we derive the corresponding holographic entanglement entropy formula. We show that the fluctuating Weyl mode does not contribute additional entropy. The entropy of the full boundary is therefore the Bekenstein-Hawking entropy, and the entropy of a boundary subregion continues to obey the Ryu-Takayanagi prescription, namely, the area of a minimal surface divided by $4G_N$. We carry out explicit calculations for global AdS, rotating and non-rotating BTZ geometries. For an interval in AdS$_3$ we find that the $K$-dependent holographic entanglement entropy is governed by $c_m=\frac{3 \ell}{2 G_N}.$ For a thermal state at high conformal temperatures we find that, the entropy is governed by $c_{\rm eff}=\frac{3 \ell}{2 G_N} \frac{K \ell- \sqrt{K^2 \ell^2-4}}{2}$, the same effective central charge that governs the Cardy-like density of states, in agreement with previous results in the literature. Finally, we also compute the entanglement entropy directly from the conjectured dual boundary theory - a holographic CFT coupled with time-like Liouville theory and deformed by a marginal $T \bar{T}$ like operator - and find $S_{EE} =\frac{c_{\rm eff}}{3} \ln\!\left(\frac{2 R \sin\phi_0}{\epsilon}\right) .$ This result for the state with no operator insertions (vacuum state ), provides an independent boundary realization of $c_{\mathrm{eff}}$ while clarifying that this state is not the state dual to global AdS.

Topologically ordered phases naturally realize quantum error correction through nonlocal encoding of quantum information. More recently, conformal field theories have been shown to realize approximate quantum error-correcting codes, but such constructions generally require fine tuning to criticality. Here we introduce a family of approximate quantum error-correcting codes realized by the chiral edges of two-dimensional topologically ordered phases. The proposed encoding combines the robustness of a gapped topological bulk with the flexibility of gapless edge conformal field theories. To characterize its robustness, we study coherent-information loss under local erasure. We derive an exact expression relating coherent-information loss to relative entropy, reducing the recoverability problem to universal properties of the edge theory. This leads to power-law scaling of coherent-information loss with the size of the erased region. We further show that, for geometrically local erasures near one edge, the two-dimensional chiral edge code is at least as robust as the dimensionally reduced CFT code, and is strictly more robust in several representative examples. For Abelian code subspaces, we further construct a power-law-range recovery map supported on the erased region together with a power-law-range buffer; this recovery map depends only on the code subspace, not on the unknown encoded state. We provide numerical calculations for lattice realizations of compact free boson and Ising CFT examples that support the theoretical predictions of the power-law exponents.

Lorentz symmetry and gauge symmetry constitute the mathematical cornerstones of modern physics, yet their ultimate physical origins remain elusive. From the standpoint of a constructive interpretation, this paper demonstrates that both symmetry structures can emerge isomorphically from a unified classical source: dynamical constraints on wave-packet excitations in a continuous elastic substrate medium (SM). Neither symmetry is posited as fundamental, nor does their emergence rely on quantization. Three core results are established. First, taking the transverse wave speed of a homogeneous, isotropic SM as the benchmark under a conventionalist synchronization scheme, Minkowski-type spacetime arises isomorphically, with Lorentz transformations as effective coordinate transformations between inertial frames. This reinterprets the Michelson–Morley null result: observers are composite wave-packet excitations, and medium-induced kinematic corrections are encoded in their measurement frameworks. Second, for wave packets endowed with $SU(N)$ intrinsic symmetry, the requirement of identity invariance drives the SM to spontaneously generate gauge fields. This requires invariant equivalence classes of intrinsic states under propagation, yielding gauge structures isomorphic to Yang-Mills theory. The gauge group $SU(N)$ is uniquely determined by the number of stable normal modes supported by the medium. Third, through the same conventionalist measurement protocols, inhomogeneous distributions of the SM emerge isomorphically as curved spacetime geometry, governed by Einstein-type field equations from variational extremization of the medium's deformation free energy. This paper advances a unified interpretive account of the physical origin underlying the mathematical structures of both Relativity and the Standard Model.

We investigate dark matter admixed neutron stars in which the neutron star coexists with an anisotropic dark matter halo described by the Einasto density profile, a model recently shown to produce regular, singularity-free black hole solutions~[Phys. Rev. D 113, 043011 (2026)]. Solving the modified Tolman–Oppenheimer–Volkoff equations with two different equations of state (BSk19 and SLy4), we find that the dark matter halo significantly alters the neutron star structure. Furthermore, for a specific range of halo parameters, $g_{rr}^{-1}$ changes sign outside the stellar surface, forming an event horizon with the neutron star persisting as a regular configuration inside it— “neutron stars in black holes”. This configuration appears in both equations of state and does not depend on a specific choice of the equation of state. The discovery of this configuration provides a new perspective and a concrete computable instance for the study of what lies inside a black hole.

I analyze the pseudoreal confining $\mathcal{N}=1$ SUSY gauge theories deformed by anomaly mediated SUSY breaking (AMSB). Taking the conjecture that the AMSB and non-SUSY limits are in the same universality class, I find broadly that the non-SUSY confining pseudoreal gauge theories of this class have no massless vectors in their spectra, and that all but one are fully gapped. This contradicts recent expectations from tumbling. I explore whether or not non-standard tumbling could reconcile the two pictures, and find that it would require condensation in repulsive channels in three of the cases, and that in one case it would require condensation in a higher-order channel. I briefly comment on the additional theories that may be in the conformal window, and find that their SUSY versions are consistent with flowing to superconformal fixed points.

A freely moving quantum Hall (QH) interface may end on a physical edge or topological boundary, but fixed-edge theory cannot determine what endpoint data make such a termination consistent. Here we formulate an open-worldsheet junction framework in which the embedding, material charge, anomaly flow, and topological boundary condition are organized together. The endpoint is specified by a geometric support and variational boundary data, together with condensable topological sectors and any outgoing channels required to absorb or continue the worldsheet flux. This construction extends the charge–shape relation to an interval and shows why a lone chiral Majorana cannot terminate on a finite-dimensional endpoint degree of freedom. It gives an operational definition of a QH brane and a systematic basis for endpoint and network theories of dynamical QH interfaces.

A Moore–Read interface carries a chiral Majorana mode on a boundary whose geometry may itself fluctuate. Fixed-edge theory does not determine how this neutral mode should be transported when the interface bends and moves, or how its dynamics couples to the fluctuating shape. Here we construct a spatially reparametrization-invariant Majorana theory on the nonrelativistic worldsheet of a freely moving interface. The changing line element fixes a universal half-density transport law, while additional curvature- and velocity-dependent couplings remain controlled by microscopic interface physics. The resulting framework identifies the Majorana stress tensor as the mediator between neutral and geometric dynamics and provides the neutral sector needed for effective theories of dynamical non-Abelian quantum Hall interfaces.

A freely moving quantum Hall interface is fundamentally different from an ordinary edge fixed by an external confining potential. Since a normal displacement changes the areas occupied by the adjacent incompressible phases, the interface geometry and charge dynamics cannot be treated as independent degrees of freedom. We formulate this problem for interfaces between Abelian quantum Hall phases using a spatially reparametrization-invariant worldsheet description, in which tangential motion is a relabeling of the interface while normal motion is physical. Starting from the two-sided Chern–Simons response, we derive the relation between normal charge transport and interface motion. We then introduce a relative-area construction, defined with respect to a material reference curve, that converts this velocity relation into an equal-time constraint linking the charged boundary sector to the interface shape. Combined with the folded $K$-matrix current algebra, this identifies the universal Hall kinematics of the moving interface while leaving its geometric energy and neutral dynamics dependent on microscopic interface physics. The resulting framework provides a systematic basis for effective theories of dynamical quantum Hall interfaces.