Papers

Global fits of the Standard Model Effective Field Theory are challenged by the large number of operators, while any given database constrains only a small subset. Selecting relevant operator hypotheses therefore requires theoretical insight into operator correlations and the sensitivity of observables. We present llm4smeft, an open source framework that addresses this problem by combining a language model, fine-tuned on the SMEFT literature, with retrieval augmented generation based on quantitative summaries of SMEFiT package global fits. Given a set of observables, the framework proposes candidate relevant operators together with their corresponding Fisher information, while retrieval ensures that model outputs are grounded in existing fit results whenever available. The framework runs in an interactive mode in which accepted hypotheses are stored in a growing knowledge base. We publicly release the llm4smeft package together with the fine-tuned language model, in which the entire framework runs locally, requiring neither internet access nor paid cloud services.

The subsystem-size dependence of ground-state entanglement entropy and its crossover to thermal entropy as a function of temperature are well understood for one-dimensional (1D) gapless systems described by conformal field theory (CFT), and for free fermions with a Fermi surface in any dimension. However, little is known about the entanglement entropy for gapless fermionic systems without quasi-particles, such as a strange metal. Here we study the entanglement entropy of fermions in a solvable large-$N$ 1D lattice model akin to the Yukawa-Sachdev-Ye-Kitaev (Yukawa SYK) model. In this model, two Fermi points are coupled to scalar bosons via spatially random Yukawa interactions, providing a solvable model of a strange metal when the bosons become critical at a quantum critical point. We exactly compute the second Rényi entropy of fermions in a spatial subregion in this model. Our results unravel crucial role of intra-subregion entanglement between fermionic and bosonic degrees of freedom along with the inter-subregion entanglement in understanding the ground states of such strongly coupled fermion-boson systems. We show that the crossover from thermal entropy to entanglement entropy, is captured by a single scaling ansatz, that collapses the second Rényi entropy of fermions for different subregion sizes and temperatures into a single universal curve. We further show that the universal scaling curve for the critical strange metal is well described by the standard CFT formula, albeit with an effective central charge substantially larger than the non-interacting value.

We construct non-commutative deformations of field and gauge theories based on star-products implemented by Drinfel'd twists. We are able to encompass a large family of twists, including those built out of conformal symmetries and supersymmetries. The main idea behind our construction is to work with twists constructed from symmetries of the undeformed theory, that are realised as active symmetry transformations. We argue that our construction amounts to a reformulation of known deformations of gauge theories, and that it significantly extends the range of applicable examples. To ensure consistency with gauge invariance, we also identify a unimodularity condition that is weaker than the one that is normally employed in the literature, so that we can apply twists that would otherwise be left out. Finally, we also prove a planar equivalence theorem stating that the Feynman diagrams of the deformed theories retain an undeformed internal structure, with the twist acting only on their external legs. All these results are important to identify and work with deformations of $\mathcal N=4$ super Yang-Mills that are proposed to be dual to homogeneous Yang-Baxter deformations of the $AdS_5\times S^5$ superstring, but the applicability of our construction and results goes beyond that.

Being agnostic about the field content of a gravitational system, we consider a general disformal transformation of the metric, $g_{\mu\nu}=C h_{\mu\nu}+D t_{\mu\nu}$, on a four-dimensional Lorentzian manifold. Using the Cayley-Hamilton theorem, we derive an explicit formula for the inverse disformed metric. Implementing the Hawking-Ellis classification, we categorize disformal transformations into four types: Type I, II, III, and IV, based on possible Jordan block structures. We further identify the Segre subclasses from the eigenvalues. We derive explicit relations between the Cayley-Hamilton degree of $t_{\mu\nu}$, its Hawking-Ellis type, and its Segre subclass, restricting the possible types from the degree alone. In some cases, the type can be determined without even performing a full Jordan decomposition. For singular transformations, when new dynamical degrees of freedom emerge, we obtain the form of their corresponding mimetic energy-momentum tensor $T^\star_{\mu\nu}$. Within the polynomial sector, the Hawking-Ellis types of $t_{\mu\nu}$ and $T^\star_{\mu\nu}$ always coincide for Type I. For Types II and III it can differ, while Type IV is preserved generically but can reduce to Type I when the complex pair is mapped to a repeated real eigenvalue. This makes it possible to infer physical properties of $T^\star_{\mu\nu}$ directly from the Hawking-Ellis type of $t_{\mu\nu}$. We apply our setup to scalar and gauge fields. We find a new pure-disformal scalar-gauge family yielding irrotational perfect fluids, including barotropic fluids with an arbitrary constant equation-of-state parameter. Two scalar fields realize all four types and the reductions from Types II and IV to Type I. This framework applies to the kinematical and dynamical study of invertible and non-invertible disformal transformations with different field content.

We study a $\mathscr{PT}$-symmetric non-Hermitian multichannel Kondo model consisting of a pair of spin-$\frac12$ impurities coupled to $n$ conduction-electron channels through complex-conjugate Kondo couplings. The impurity renormalization-group (RG) flow is characterized by the Kondo scale $T_K$ and a dimensionless non-Hermiticity parameter $\alpha$. As $\alpha$ increases, the exact Bethe Ansatz solution exhibits four impurity phases: overscreened Kondo, zero mode, Yu–Shiba–Rusinov (YSR), and local moment. The Kondo, zero-mode, and local-moment phases are $\mathscr{PT}$-unbroken, whereas the YSR phase spontaneously breaks $\mathscr{PT}$ symmetry. Using a generalized thermodynamic Bethe Ansatz, we determine the impurity free energy and Affleck–Ludwig $g$-function throughout the $\mathscr{PT}$-unbroken phases. In the Kondo phase, the defect RG flow connects the ultraviolet and infrared conformal fixed points, with the impurity entropy flowing from $2\ln2$ to $2\ln\left[2\cos\left(\frac{\pi}{n+2}\right)\right]$, in agreement with defect conformal field theory. In the zero-mode phase, zero-energy impurity strings reorganize the spectrum into multiple excitation towers, while in the local-moment phase, the RG flow becomes cyclic, returning to the unscreened local-moment fixed point. We conjecture that RG irreversibility, and hence a generalized Affleck–Ludwig $g$-theorem, survives throughout the Kondo phase. Our exact solution nevertheless shows that a real spectrum and defect entropies consistent with defect CFT do not guarantee RG irreversibility: the impurity entropy is non-monotonic in both the zero-mode and local-moment phases.

I study constraints from consistent complex factorisation of $2\rightarrow 2$ scattering amplitudes in $4d$ and their relationship with supersymmetry. I complete the argument demonstrating that a massless helicity-$3/2$ particle must be a gravitino in a theory of supergravity and derive the structure and couplings of massive supermultiplets from first principles. For massive BPS particles in theories with extended supersymmetry, further constraints on the couplings are derived from consistent factorisation of massive superamplitudes. Among these is the requirement that BPS vector bosons must have couplings conforming to Lie algebra structure constants or generalised Chern-Simons terms. The gravitational coupling is shown to participate and draws the graviphotons into the Lie algebra. All $2\rightarrow 2$ tree-level amplitudes of massive particles with spin $s\leq 1$ are calculated in (super)gravity using on-shell methods and the double copy. These are assembled and decomposed into (super)amplitudes with varying amounts of supersymmetry. Finally, I study scattering of BPS gravitinos with unbroken $\mathcal{N}\geq 4$ supergravity and show that consistent factorisation leads to the full reconstruction of the super-Higgs mechanism. This argument completely determines the perturbative structure of all $\mathcal{N}=4$ Minkowski vacua of gauged maximal supergravity. Gravitinos in theories not admitting a super-Higgs mechanism are ruled-out.

We point out that the asymptotically Bertotti-Robinson multi-black hole solutions of Einstein-Maxwell theory can be constructed using only three-dimensional sigma-model techniques, without resorting to the monodromy-matrix approach.

We calculate the vacuum polarization energy (VPE) of a scalar field in the background of a nonsingular cosmic string in $2+1$ spacetime dimensions. Our calculation expresses the VPE as a renormalized sum and integral over scattering data, which can be expressed in terms of Legendre and Bessel functions for the "ballpoint pen" model, analogous to a square well in curvature, and which can be obtained numerically for a generic string profile. We show how relationships between the local density of states, expressed in terms of the Green's function, and the global density of states, expressed in terms of the Jost function, extend to this curved spacetime background and allow for precise implementation of perturbative renormalization conditions.

We establish a mesoscopic local law and quantitative eigenvector-delocalization estimates for the Sachdev–Ye–Kitaev model (SYK) Hamiltonian of $N$ interacting Majorana fermions subject to a $q$-body interaction. For even $q\ll N^{\frac{1}{2}}$, we prove that the normalized Stieltjes transform is approximated, uniformly on bounded energy intervals, by an explicit deterministic profile which we construct as an asymptotic expansion in the proportion $\alpha_{N,q}$ of anticommuting $q$-body interaction terms. The result holds both on the full Hilbert space and in each fermion-parity sector. We derive mesoscopic eigenvalue counting and spectral form factor estimates. For fixed $q$, we further obtain high-probability $\ell^\infty$-delocalization bounds in any deterministic orthonormal basis for individual bulk eigenvectors. These are the first mesoscopic laws and eigenvector delocalization estimates for the SYK Hamiltonian, which we obtain using the resolvent method.

We compare two currently known examples of hyperbolic SU(2) two-monopole metrics and their candidacy as models of hyperbolic monopole dynamics. The first is Sutcliffe's boundary metric and the other is a well-known self-dual Einstein metric found by Hitchin. We show that these metrics are conformally inequivalent and make significantly different predictions for monopole dynamics. We compare each metric to the Franchetti-Ross point particle approximation of hyperbolic monopole dynamics. We show Sutcliffe's metric does not converge to the point particle approximation in the large separation limit. We also check Sen's conjecture for each metric by computing their $L^2$ harmonic two-forms. By a symmetry argument we are able to show that Hitchin's metric has a single $L^2$ harmonic two-form consistent with the conjecture.

We derive the leading logarithmic soft-photon theorem in $d>4$ spacetime dimensions and its classical radiative counterpart. A direct one-loop analysis in massive scalar quantum electrodynamics (QED) yields a factorizing soft term of order $\omega^{d-4}\ln\omega$, although the charged-particle S-matrix is infrared finite. The logarithm is generated by the scale-invariant loop-momentum region $\omega\ll|\ell|\ll\Lambda$, where $\Lambda$ denotes a characteristic hard-particle energy scale. At leading radiative order, the corresponding logarithmic contribution to the classical electromagnetic waveform arises from the long-range acceleration of the asymptotic charged particles. In even $d\geq6$, the straight-line waveform at this radiative order is distributionally supported in retarded time within an interval whose width is set by the characteristic size of the hard-scattering region, whereas the logarithmic acceleration term produces universal early- and late-time radiative tails proportional to $|u|^{-(3d-10)/2}$. In odd $d\geq5$, straight-line motion already gives a late-time tail at the same radiative order proportional to $u^{-(d-4)/2}$. The acceleration correction adds universal late- and early-time terms proportional, respectively, to $\ln u/u^{(3d-10)/2}$ and $|u|^{-(3d-10)/2}$. A comparison of Feynman and retarded boundary conditions separates the classically radiative contribution from the intrinsically quantum part of the logarithmic soft factor.

We present a numerical computation of the two-loop QCD scattering amplitudes for the production of a top-antitop quark pair in association with a $W$ boson ($t\bar{t}W$) at the LHC in the generalised leading-colour approximation, retaining the exact dependence on the top-quark and $W$-boson masses. Rather than pursuing a fully analytic calculation, we employ a hybrid framework that combines numerical evaluation with strong algebraic and analytic control, allowing ultraviolet and infrared singularities as well as large intermediate cancellations to be treated exactly. This is achieved by expressing the finite remainder in terms of a set of special functions with rational coefficients. The special functions are evaluated numerically by solving differential equations through power-series expansions, while the values of the rational coefficients are reconstructed, point by point, from finite-field evaluations. The calculation is performed in the 't Hooft-Veltman scheme and validated against an independent implementation in conventional dimensional regularisation employing a substantially different computational strategy. We finally provide the colour- and polarisation-summed hard functions evaluated on the phase-space grid used in a previous computation of the next-to-next-to-leading-order QCD corrections to the $t\bar{t}W$ cross section.

Gravitational-wave (GW) cosmology is currently bottlenecked by the scarcity of electromagnetic counterparts for bright sirens and the systematic uncertainties of galaxy catalogs for dark sirens. We propose a purely gravitational resolution using the Integrated Cosmological Memory (ICM)-the cumulative GW strain encoded in the spacetime geometry of an expanding Universe. While the GW transient emitted by the source provides the luminosity distance, the ICM accumulates a mathematically distinct integral of the cosmic expansion history. We demonstrate that extracting both observables from a single binary merger completely breaks the distance-redshift degeneracy within the gravitational sector. This establishes a novel, catalog-free dark siren framework for third-generation GW detector networks. Crucially, the resulting constraints on late-time dark energy are only weakly sensitive to the local expansion rate, providing a robust cosmological probe that can potentially mitigate the impact of the H0 tension.

Departures from standard slow-roll (SR) inflation have attracted increasing interest in recent years. In particular, scenarios that strongly enhance the power spectrum of the curvature perturbation are often proposed as a mechanism for producing primordial black holes, which could account for part or the totality of dark matter. An ongoing debate in these models is whether non-linear interactions of cosmological perturbations on small scales, namely loop corrections, can become sufficiently large to backreact on CMB scales. In this work, we adopt a non-linear framework, dropping spatial-gradient terms, to study loop corrections at super-Hubble scales. Our focus is to clarify the role of spatial-diffeomorphism invariance, especially dilatation invariance, which is the symmetry under overall rescaling of spatial coordinates, in demonstrating the suppression of loop corrections to the CMB power spectrum. This analysis is valid for any inflaton potential, both with smooth and sharp transitions, and at any loop order, as long as the CMB scales cross the horizon during an SR phase. We compare this result with the different explanations proposed in the literature using various gauge choices, and show our analysis is consistent both in the comoving and in the spatially-flat gauges. In particular, we show that in the spatially-flat gauge, the cubic interaction contains a term that diverges in the sharp transition limit. However, this contribution is exactly cancelled by the quartic interaction.

We provide a cluster algebraic construction of the cube root symbol letters that appear at leading order in the near-collinear expansion of the four-point energy correlator in $\mathcal{N}=4$ SYM theory.

The lightlike Wilson line cusp underlies the Sudakov double logarithm and is a central ingredient in gauge-theory factorization. We ask what replaces this behavior for general conformal line defects in Lorentzian signature. We argue that, when the defects admit local endpoint operators, the cusp anomalous dimension has a finite large-boost limit fixed by the scaling dimensions of the corresponding defect-creation operators. We further analyze the distinct analytic continuations of the cusp, elucidate their physical interpretations, and derive a positivity condition on the Lorentzian cusp anomalous dimension. We test these predictions in several perturbative examples, including pinning-field defects and spin impurities, and discuss their possible implications for gauge theories.

Two-dimensional incompressible fluids conserve energy and enstrophy in the inviscid limit. Fjørtoft's argument uses this pair to constrain nonlinear energy transfer. We examine the corresponding question in General Relativity using the magnetic Weyl functional $\mathcal Z=\int B_{ab}B^{ab}\sqrt{\gamma}\,d^3x$. Its transverse radiativ e part carries an additional frequency-squared weight relative to gravitational-wave energy: $\delta\mathcal Z_k\simeq\omega_k^2W_k$ in the radiation zone, with $W=8\pi G E_{\rm GW}$. We derive its balance law from the Bianchi identities, obtaining the algebraic cancellations, bulk sources and boundary fluxes. Conservation of positive e nergy and curvature norm through nonlinear transfer gives a Fjørtoft constraint when their weights are ordered. Resonant weak-wave interactions generally change the c urvature norm; $2\leftrightarrow2$ dynamics instead conserves energy and wave action. We examine the competition between transfer and linear losses in Kerr and AdS backg rounds, where long-lived or confined modes provide time for nonlinear evolution. In the hydrodynamic regime of AdS$_4$, a fluid-weighted magnetic Weyl functional inherit s fluid enstrophy conservation in the inviscid limit. We compute its proportionality coefficient to boundary enstrophy in closed form at leading gradient order, giving a bulk diagnostic for holographic turbulence.

String compactifications generically produce ${\cal O}(100)$ light axion-like particles, yet low-energy mixing has not previously been exploited as a structuring constraint on their spectrum. We show that the requirement of well-defined QCD-induced mass mixing forces the axion masses into a hierarchically spaced ordering, while stochastic mixing organizes the decay constants into a hierarchically split distribution – two populations separated by an essentially empty window. Both patterns are insensitive to ultraviolet input and satisfy the relevant Swampland constraints within standard large-volume compactifications. We term this emergent pattern the hierarchical axiverse.

In integration-by-parts reduction of Feynman integrals, the order relation in the Laporta algorithm determines a set of master integrals. In this paper we investigate the intersection matrices of the integrands of the master integrals that are obtained from a geometric order relation. With an appropriate definition of integrands and their duals, we find that the intersection matrices are simpler than expected: For a filtration-compatible basis, the entries of the intersection matrix are Laurent polynomials in the dimensional regularisation parameter $\varepsilon$. For an $\varepsilon$-factorised basis, the entries are instead integers, up to an overall power of $\varepsilon$, if the boundary values for the auxiliary functions of the rotation are chosen appropriately. This has practical consequences: We can systematically eliminate certain auxiliary transcendental functions, introduced in going from a filtration-compatible basis to an $\varepsilon$-factorised basis. We provide an algorithm that performs this elimination while minimising the number of required calculations.

An isolated occupied multiplet may admit local tensor-product descriptions without a globally consistent subsystem structure. We characterize the obstruction by comparing the transition functions of the occupied multiplet with those generated by independent basis changes in the two candidate subsystems. When a decomposition into rank-one sectors over a closed surface is specified, the resulting quotient removes row- and column-additive Chern data and yields mixed Chern classes. Momentum-dependent mixing of the sector labels adds the Gauss–Codazzi curvature of the moving lines, while in the label-conserving limit the mixed class is measured by a crossed Thouless pump. When only the factor dimensions $p$ and $q$ are specified, the comparison is made at the level of the clutching map of a rank-$pq$ bundle over $S^4$. Product frames generate winding numbers in $q\mathbb Z+p\mathbb Z$, so global factorization is possible exactly when $C_2$ is divisible by $\gcd(p,q)$; in particular, odd $C_2$ obstructs a $2\times2$ factorization. We illustrate the two settings with finite eight-level Hamiltonians and give pumping and occupied-projector tomography protocols for their readout.

We develop a general-relativistic framework for two-component quantum dark fermion stars: equilibrium configurations of two degenerate fermion species governed by gravity, a Yukawa-mediated dark fifth force and a globally relevant Bohm quantum-pressure correction. The treatment retains the full covariant form of the nonlinear Klein–Gordon equation in the Schwarzschild interior, with closure relations valid at arbitrary compactness, from the ultralight baseline up to densities of order $0.16\,\mathrm{fm}^{-3}$ at which relativistic scalar densities and self-consistent effective fermion masses become unavoidable. Two Lagrangian parameters, the dark-fermion mass and the dimensionless ratio between the Yukawa channel and gravity, together fix the equilibrium structure; a joint measurement of mass and radius therefore constrains the dark-sector microphysics directly from gravitational-wave observables. For particle masses in the band $10^{-11}$–$10^{-10}$ eV, the configurations exhibit radii of $3$-$24\,\mathrm{km}$ and compactness in the range $0.14$-$0.34$, behaving as dual mimickers: at moderate compactness they overlap with neutron stars in mass, radius, and inspiral frequency; at the most compact end ($\kappa\sim 0.34$, $R_T/R_S\simeq 1.5$) they cross the photon sphere and could masquerade as low-mass black holes in the mass-gap region. Tidal-deformability measurements discriminate against both populations: the dimensionless tidal deformability is measurably smaller than the neutron-star value yet remains non-zero, unlike that of a genuine black hole. These objects populate the sensitivity bands of LISA, the Einstein Telescope, and Cosmic Explorer, producing astrometric microlensing signatures individually resolvable by Gaia. The framework thus provides a reproducible and falsifiable template for constraining dark-sector properties through multi-messenger observations.

Recent numerical studies of semiclassical gravity suggest that, in spherically symmetric black holes with both outer and inner horizons, the semiclassical instability of the inner horizon can drive the complete evaporation of the trapped region on timescales shorter than the standard Hawking evaporation time. Independent simulations further indicate that the disappearance of the trapped region is followed by the formation of an anti-trapped region, i.e.~a dynamical white hole. In this work, we develop an analytic treatment of quantum effects in trapped and anti-trapped regions, showing how these numerical results can be understood within simplified two-dimensional models. We consider collapse models describing the formation of charged and regular black holes and compute the renormalized stress-energy tensor of the $|\textit{in}\rangle$ vacuum state. We show that, within this framework, the emergence of an anti-trapped region is a generic consequence of the amplification of negative energy fluxes propagating along the outgoing direction inside the initial trapped region. This provides an analytic explanation for the black-hole-to-white-hole transition observed in numerical simulations. Our analysis further suggests that the fluxes generated by the subsequent anti-trapped region, now propagating along the ingoing direction, may trigger the formation of a new trapped region. This raises the possibility of a cascade of black-to-white-hole transitions, potentially ending in a horizon-free, bouncing spacetime without invoking additional quantum-gravitational dynamics. Although establishing the complete evolution requires a self-consistent treatment of semiclassical backreaction, our framework identifies which features of the mechanism are universal and which depend on the geometry, laying the groundwork for a systematic investigation of semiclassical black-hole-to-white-hole transitions.

We study whether varying the topological boundary of the doubled Virasoro TQFT can produce distinct torus pairings for an ensemble interpretation of 3D gravity. In the ordinary nondegenerate sector, every bounded pairing that commutes with the modular transformations is scalar, and vacuum normalization selects the diagonal pairing. The proof identifies the modular transformations with the even Weil representation and applies the Cowling–Steger lattice-restriction theorem. Under the ordinary block-diagonal vacuum–continuum ansatz, positivity and the two vacuum marginals also make a Borel-measure pairing bounded, without assuming absolute continuity; modular invariance then forces the same diagonal pairing. These two classes therefore contain no distinct torus pairings to average. A nontrivial Virasoro boundary ensemble must involve genus-one data outside these classes, additional sectors or vacuum–continuum couplings, or information invisible in the torus pairing. Elementary proofs in explicit regular sectors explain the rigidity mechanisms, and numerical calculations provide independent checks.

We study the geometry of mixed fields, consisting of a connection and a $B$-field on a principal circle bundle over a Riemann surface, from the perspective of gauge theory and T-duality. Motivated by the foundational work of Atiyah–Bott and Segal, we introduce a twisted Yang–Mills functional whose critical locus, in the flat case, is governed by the simultaneous vanishing of the curvature and the $H$-flux. We show that the gauge group is a semi-direct product of abelian groups parametrised by an integer $\lambda$. The moduli spaces are constructed by presymplectic reduction and shown to be Heisenberg contact manifolds for $\lambda \neq 0$, whose topology we characterise completely. We show that T-duality preserves the twisted Yang–Mills functional and acts on the configuration space of flat mixed fields. We identify the subgroups of gauge transformations that are compatible with the T-duality map and describe the induced action on the singular quotient of T-dualizable flat mixed fields. Precisely at $\lambda =1$ does T-duality descend to an involutive contactomorphism of the moduli space.

Unitary matrix models, among other things, play an important role in representing the irregular conformal block and hence LEEA of some asymptotically free susy gauge theories. Here, we develop a method of how to determine the qualitative structure of phase diagram by the deformation of classical potential, and illustrate this by the examples that contain term up to $\cos n\alpha$, $n \leq 3$. We point out that a set of $\beta$ functions on critical “lines" is nowhere a vanishing vector. This generalizes the $n =1$ GWW case and tells us the third order (rather than second order) phase transition in conformity with the range of values for the susceptibility exponent.

We investigate the conservative dynamics of relativistic charged particles in a Schwarzschild spacetime threaded by an externally supported dipolar magnetic field. The gravitational sector is treated exactly in isotropic coordinates, while the electromagnetic field is described by the leading asymptotic term of the relativistic exterior dipole solution. This formulation provides an analytically tractable relativistic extension of the classical Størmer problem and allows the circular-orbit and stability structure to be studied explicitly. For the outward-Lorentz branch, characterized by a positive signed magnetic coupling for positive azimuthal motion, we find a non-trivial competition between radial and vertical stability. Weak magnetic coupling shifts the radially marginal orbit inward, whereas at stronger coupling vertical instability becomes the limiting mechanism and the inner boundary of stable circular motion moves outward. The associated vertical epicyclic mode progressively softens and vanishes at the vertical stability boundary. The marginally bound sequence exhibits a distinct strong-coupling behaviour, illustrating that energetic and stability boundaries need not evolve together. The radial and vertical epicyclic frequencies also generate characteristic commensurabilities that may provide natural sites for nonlinear orbital coupling. Because the magnetic field is treated as a test field, these charged-particle effects leave the vacuum Schwarzschild null-geodesic structure unchanged. Magnetic signatures in compact-object observations must therefore arise through the dynamics and radiation of charged matter, plasma propagation effects, or physics beyond the test-field approximation. The framework developed here provides an analytical basis for studying nonlinear dynamics, radiation reaction, and more realistic compact-object magnetospheres.

We study the minimal classically scale-invariant extension of the Standard Model, containing a single $\mathbb Z_2$-stabilised real scalar singlet whose mass is not an independent input but is generated dynamically through the quantum effective potential and linked to radiative electroweak symmetry breaking through the Higgs portal. We construct the full two-field one-loop effective potential and introduce a modified on-shell renormalisation scheme that fixes the electroweak vacuum, the Higgs mass, the vanishing Higgs–singlet mixing and the singlet curvature at the physical point, yielding predictions stable under renormalisation-scale variation. Since thermal freeze-out is excluded by direct-detection limits, we identify a highly predictive freeze-in realisation of this model. Imposing perturbativity, vacuum stability and the observed relic abundance leads to a freeze-in solution with a dark-matter mass of around $2~{\rm MeV}$. The predicted electron-scattering cross section for this solution lies far below the current sensitivity of DAMIC-M. Current direct-detection experiments therefore do not constrain this scenario. The minimal scale-invariant singlet model thus provides a robust and highly predictive framework connecting radiative electroweak symmetry breaking and freeze-in dark-matter genesis.

We systematically investigate and compare the worldsheet actions, BRST structures and the quantum anomalies of four different formulations of tensionless ($T = 0$) bosonic string theory: the $(D+2)$-dimensional conformal string \cite{Gustafsson:1994kr}, the $D$-dimensional ILST null string \cite{Isberg:1993av}, the $D$-dimensional Carroll-Weyl gauged string \cite{Sheikh-Jabbari:2026vqh, Sheikh-Jabbari:2026tpf}, and the $D$-dimensional hybrid null string \cite{Chen:2026klv}. By expressing all fields and constraint generators strictly in terms of mode expansions and adopting a unified algebraic framework, we analyze their quantum anomalies under two distinct worldsheet vacua: the induced vacuum and the flipped vacuum. With the BRST-compatible vacuum definition and the symmetric $\alpha=0$ zeta prescription, we show that no critical dimension is inferred from the vanishing of the quantum anomaly in the induced vacuum. In contrast, the flipped highest-weight vacuum leads to non-trivial constraints, reproducing the critical dimension $D=26$ for the ILST null strings, a $\lambda$-dependent critical dimension $D(\lambda)$ for the hybrid null string whose range covers every positive integer $D\geq 4$ (reproduces $D=26$ at $\lambda=1$), and more importantly showing that the conformal string and the Carroll-Weyl gauged string are structurally anomalous with no consistent critical dimension due to the discrepancy of their central charge parameters $\tilde d_i$. Furthermore, the ILST null string model has target-space conformal symmetry $SO(D,2)$, the ghost-completed $SO(D,2)$ charges are closed on the induced-vacuum BRST cohomology in the $\alpha=0$ prescription, whereas the symmetry is quantum mechanically broken in the flipped vacuum.

We present an advancement for solving the Discretized Light-Cone Quantization (DLCQ) Hamiltonian for mass spectra in 2D $\phi^4$ theory that incorporates perturbative zero-mode contributions. We demonstrate that this correction accelerates numerical convergence of the mass eigenstates with increasing resolution and yields a critical coupling of comparable accuracy with a substantial reduction in computational costs. Specifically, with more than one order of magnitude reduction in basis space dimensionality we achieve an extrapolated critical coupling of $23.10 \pm 0.25$ compared with $23.53 \pm 0.26$ in the larger basis but without zero-mode correction. We employ Gaussian Process Regression for extrapolation to the continuum limit. The approach we present here is prospective for studies of higher-dimensional gauge theories.

We study static and slowly rotating traversable wormholes embedded in two contrasting dark matter environments, the cuspy Navarro-Frenk-White (NFW) halo and the cored solitonic wave dark matter ($\psi$DM) profile, using observational parameters set by the rotation curve of the dwarf galaxy NGC\,2366. For each profile, we solve the Einstein field equations in the Morris-Thorne framework to obtain the shape and redshift functions, then extend to slow rotation via the Teo metric with a Lense–Thirring frame-dragging term. Across the four resulting spacetimes and six throat radii, we trace null geodesics, compute specific intensity profiles and polar shadow maps, and construct accretion disk images including the full relativistic Doppler effect. We noticed these two profiles differ sharply in photon dynamics. The NFW potential is too shallow to support a detached photon sphere, so its critical impact parameter stays close to the throat radius. The soliton core, by contrast, is focused enough to host a genuine unstable photon orbit that raises the critical impact parameter to about $1.18$–$1.26$ times the throat radius. This difference in photon-sphere structure propagates through nearly every observable, including photon-ring sharpness, shadow size, accretion-disk appearance, and, in the rotating case, the degree of shadow asymmetry from frame dragging. The soliton shadow size also tracks the mass of the underlying ultralight boson through $\rho_c\propto m_b^{-2}$, with a transition from total capture to mainly deflecting lensing near $m_b\sim10^{-18}$\,eV, a feature absent for NFW that offers a direct probe of dark matter microphysics. These results show that wormhole photon dynamics are shaped by the dark matter profile, pointing to a possible observational route to probe the nature of dark matter.