Papers

We analyze a simple extension of the Schwinger model, which we refer to as the $p$-Schwinger model, on a de Sitter background. In this theory, the charged massless fermions carry non-unit integer charge $p$. In Minkowski space, the $p$-Schwinger model has discrete zero- and one-form global symmetries that are spontaneously broken, yielding $p$ degenerate ground states. We demonstrate that these features persist upon placing the $p$-Schwinger model on a global de Sitter background, establishing that such discrete global symmetries can be spontaneously broken for quantum field theories in de Sitter space. In particular, the theory is endowed with $p$ distinct, but locally-indistinguishable, de Sitter invariant states, the de Sitter vacua, satisfying the Hadamard property. We couple a variant of the $p$-Schwinger model with ${\rm N}_{\rm f}$ flavors to quantum gravity with $\Lambda>0$, and demonstrate the existence of a semiclassical de Sitter saddle at large ${\rm N}_{\rm f}$. In the gravitational theory, the $p$ de Sitter invariant vacua are speculatively interpreted as microstates of the de Sitter horizon in the low-energy effective field theory.

We present the first complete non-redundant operator basis for the Standard Model Effective Field Theory (SMEFT) at finite temperature, using the imaginary-time formalism. By employing the Hilbert series method on the space-time manifold $\mathbb{R}^3 \times S^1$, we classify all effective operators up to dimension-six. In constructing the basis, we consistently impose integration-by-parts and equations-of-motion constraints along spatial directions. We further analyze the impact of additional constraints, including the vanishing of the curl of the electric and magnetic fields and gauge choices for the temporal components on an operator basis. We also realize them in terms of static three-dimensional spatial and zero-temperature SMEFT operators. At dimension five and six, we identify intrinsically thermal operators that vanish with temperature. Our framework is fully general and extends to arbitrary mass dimension and compact connected internal symmetry groups.

The goal of this note is to show that Jordan algebras and superalgebras provide an elegant and concise language for formulating quantum mechanical problems with inherent (super)conformal symmetry. The superconformal symmetries of the quantum MICZ-Kepler model and its dual oscillator realization in ${\mathbb R}^2$ are reviewed through the lens of the Tits-Kantor-Koecher correspondence: Kaplansky ${\mathfrak J} {\mathbb R}^{1|2}$ and Exceptional ${\mathfrak J} F^{6|4}$ Jordan superalgebras provide a natural framework for reconstructing (variously extended) superconformal algebras hidden in the Landau levels of an electron in an external magnetic field.

We construct the generalized Komar charge of generic, non-linear theories of electrodynamics (NLED) in 4 dimensions coupled to Einstein gravity. The contribution of the dimensionful coupling constant present in all these theories is obtained by promoting it to a dynamical field which is forced to be constant on-shell by a Lagrange multiplier. We use this charge to derive a Smarr formula for asymptotically-flat black-hole and soliton solutions of these theories that includes the contribution of the coupling constant. Previously, this contribution had been found using homogeneity arguments. We test our results on a broad class of Einstein–NLED theories and analyze in detail the thermodynamics of the regular Bardeen black hole using the conservation of the generalized Komar charge to understand the regularity of regular black holes inside the event horizon.

We introduce an analytic approach to study gravitational lensing in the presence of a distribution of hadrons. The situation is analogous to the propagation of photons in a medium with a nontrivial Cooper-pair condensate, where the photon acquires an effective mass term that may depend on the coordinates if the condensate is not homogeneous. As a result, photons generally do not follow null geodesics in the hadronic medium. In this setup, hadrons are described by the nonlinear sigma model minimally coupled to Maxwell theory. The modified Raychaudhuri equation, including hadronic corrections, is derived, along with the integral curves of probe photons in the eikonal approximation. These results are consistent with the theory of gravitational lensing in plasma media, with the advantage that transport properties, such as the refractive index, can be expressed analytically in terms of the hadronic density without assuming a phenomenological modeling thereof. As an example, we study the hadronic lensing produced by an analytic black hole sourced by superfluid pionic vortices, and we obtain the hadronic correction to the deflection angle in the weak-field limit.

The AMPS paradox assumes a globally associative tensor-product stage for the early radiation, the exterior Hawking mode, and the interior partner. We study a retained attractor sector of octonionic magical supergravity whose horizon symbols form the Albert algebra J3(O). This induces an Albertian algebraic-quantum description: states are positive normalized functionals, events are Jordan idempotents, reversible motions are algebra automorphisms, and ordinary quantum mechanics is recovered on associative readout blocks. Peirce theory then splits the horizon data into a hidden exceptional complement, an interface relay, and a two-helicity exterior detector. Eliminating the relay gives a source-fixed Volterra memory law on a neutral-source fixed-charge Reissner–Nordstrom evaporation trajectory. In real time, the leading one-time occupation follows the sourced evaporation clock, while the retained-memory imprint appears as a spectral-overlap connected two-time coherence of windowed helicity/Stokes observables in the emitted history. In Euclidean time, the Peirce–Volterra kernel becomes a transfer kernel with two branchwise superstatistical limits: a regular-opening Tsallis/Lomax onset and a near-extremal shifted-Levy residence branch. The lower admissible envelope of the endpoint actions then reconstructs the Page-curve envelope. The result is an ordinary emitted readout with exceptional memory, not a restored AMPS tensor factorization.

In this work, we explore the combinatorics arising from the quiver generating series of the unreduced $r$-colored HOMFLY-PT polynomial $\bar{P}_r(a,q)$ for some twist-knots and double twist knots. By taking the limit $a = 0$ and $q = 1$, we indeed obtain lattice path models for these knots.

The Sachdev-Ye-Kitaev (SYK) model is a disordered quantum mean-field model studied in condensed matter physics and the holographic theory of black holes. Its structural properties can be derived heuristically using a combination of the replica method and path integration techniques. Analyzing it mathematically rigorously, however, turned out to be notoriously difficult, even for basic questions such as computing the annealed free energy. In this paper we rigorously compute the free energy limit (annealed and quenched) for this model at high enough but constant temperature. Our results are in numerical agreement with the results derived by physics methods. Remarkably, though, our method of proof is novel and is different from the physics approach. It is based on (a) the theory of the component structure of sparse random graphs and (b) a variant of the cavity method, used widely in prior rigorous and heuristic treatments of classical spin glasses.

We consider the one-dimensional Dirac equation with the most general relativistic contact interaction supported on two points symmetrically located with respect to the origin. In order to determine the shape of the interaction, we use a distributional method, which in the present case is equivalent to the standard method of defining contact interactions by self-adjoint extensions of symmetric operators. The interaction on each of these two points depends on four parameters, each one having a clear physical meaning. We are interested in the scattering and confining properties of this model. We focus our attention on even or odd interactions under parity transformations and investigate the existence of critical and supercritical states, bound states, confinement and scattering resonances for some particular interactions of special interest.

In previous work, we extracted from a finite-node conifold degeneration the state-data package $A_\Sigma=(V_\Sigma,E_\Sigma,c_\Sigma)$ and then constructed the support-level interaction package encoded by a binary incidence structure and finite quiver-theoretic skeleton \cite{RahmanQuiverDataI,RahmanQuiverDataII}. The present paper introduces the next layer: a graded pairwise interaction package refining binary support. Since the support matrix records where a mediated channel is present, but not its derived size, cohomological degree, or exact-triangle behavior, we introduce mediated triangle transport (MTT). An MTT datum combines bulk-mediated schober transport, localized probes, corrected-extension shadow compatibility, and derived interaction profunctors. For each ordered pair $(i,j)$, it produces $\mathbb T_{ij}(X,Y):=\RHom_{\mathcal C_{p_j}}(\Psi_j\Phi_i(X),Y)$ and the probe interaction complex $\mathsf H_{ij}:=\mathbb T_{ij}(L_i,L_j)=\RHom_{\mathcal C_{p_j}}(\Psi_j\Phi_i(L_i),L_j)$. We prove exactness and long exact interaction sequences, isolate a triangle-visible nonvanishing criterion, and formulate a conditional bridge theorem showing that supported channels yield nontrivial pairwise interaction complexes under the stated probe, content, and detector hypotheses. Under a bounded Hom-finite convention, the cohomology of $\mathsf H_{ij}$ defines $P_{ij}(q)=\sum_m \dim H^m(\mathsf H_{ij})q^m$, and these polynomials assemble into $I_\Sigma^{\mathrm{gr}}$. Thus $(A_\Sigma,I_\Sigma^{(0/1)},I_\Sigma^{\mathrm{gr}})$ provides the first graded interaction input for later stability, BPS, and wall-crossing theory.

A recent article by Lohmiller & Slotine (Proc.\ R.\ Soc.\ A 482: 20250413) claims that the Schrödinger equation can be solved exactly using only classical least action and classical fluid density, asserting that this formulation avoids semiclassical approximations. We show that their mathematical derivation contains a foundational error. By neglecting the spatial derivatives of the probability density amplitude, the authors inadvertently omit the quantum potential – the term originally identified by Madelung and later emphasised by Bohm. Consequently, their proposed equivalence is not exact but rather constitutes the standard semiclassical approximation. We further demonstrate that each of the paper's illustrative examples either belongs to a class where the quantum potential vanishes identically due to the geometry of the problem, or recovers the correct quantum result by importing quantum eigenfunctions through the initial conditions, thereby concealing the error.

We study the backreaction of a charged scalar quantum field in the presence of two opposite charges placed at the boundaries of a finite one-dimensional region, with attention to boundary effects. We review, correct, and extend previous corresponding work of Ambjørn & Wolfram \cite{ambjorn_properties_1983}. Despite notable differences, our analysis confirms the mechanism, discussed by Ambjørn & Wolfram, by which the incorporation of backreaction avoids certain instabilities. We also observe the interesting phenomenon of “over-screening”, by which for high external charges an increase of the external charges leads to a decrease of the electric field between the two charges.

In this article, we test the validity of the weak cosmic censorship conjecture (wCCC) in the background of a quantum Kerr-de Sitter (qKdS) black hole, incorporating exact backreaction from quantum matter fields. Using a test particle approach, we analyze whether an extremal qKdS black hole can be over-extremized to expose a naked singularity. Our results indicate that the black hole remains stable against horizon-destroying processes induced by infalling matter. Quantum corrections enhance the horizon's robustness rather than destabilize it, offering further evidence that wCCC remains preserved in the presence of quantum effects.

We study nonperturbative pair production driven by alternating-sign electric field pulse trains. Using a quantum kinetic approach, we analyze both the longitudinal momentum spectrum and the particle yield for pulse sequences with either strictly periodic temporal structure, in which the pulse amplitudes alternate in a regular and repeating (E_1, E_2) pattern, or quasiperiodic (Fibonacci-ordered) structure, where the amplitudes follow a deterministic but aperiodic sequence generated by the Fibonacci substitution rule, exhibiting long-range order without exact repetition. For N=12 pulses, periodic trains generate regularly modulated spectra characteristic of multi-slit (Ramsey-type) interference, whereas Fibonacci sequences produce fragmented structures and partial momentum-space localization. Increasing the pulse number to N=20 further enhances these effects: periodic driving yields sharper and higher-contrast interference fringes, while quasiperiodic ordering leads to stronger localization and increasingly irregular spectral features.The particle yield exhibits a strongly nonlinear dependence on the field-strength ratio. For weak modulation , both temporal orderings produce nearly identical yields. For stronger fields, a modest crossover behavior is observed, with quasiperiodic sequences yielding slightly larger values than the periodic case. Overall, temporal ordering primarily redistributes spectral weight in momentum space, while the integrated yield is governed predominantly by the effective field strength. These results establish long-range temporal ordering as an effective control parameter in multipulse Schwinger pair production and provide guidance for designing tailored pulse sequences in future high-intensity laser experiments.

Quantum many-body scars are atypical nonthermal states embedded in the chaotic spectrum that evade conventional ergodicity. We propose the asymptotically AdS mini-boson star as a holographic candidate for scar-like states. Their spectrum exhibits random-matrix signatures of chaos while supporting embedded integrable spectral branches. The whole holographic system, including black holes, is generically chaotic with most eigenstates satisfying the eigenstate thermalization hypothesis; in contrast, the boson star macrostate probes a near-integrable subsector within this chaotic spectrum, signaling scarred spectral structures. Boson stars further display anomalously low entanglement relative to black holes at the same energy density, and also robust revivals in Krylov complexity, revealing nonergodic dynamics. These spectral, entanglement, and dynamical diagnostics provide unified evidence for holographic quantum scars in a self-gravitating system. Our work suggests a new connection between many-body scar physics, quantum chaos, and horizonless gravitational dynamics.

We apply the functional renormalization group to an Abelian Group Field Theory extended beyond the branched-polymer (melonic) sector by including interactions that are subdominant from a power-counting perspective but enhanced by derivative couplings. Focusing on a rank-4 model, we consider a class of non-melonic interactions with a necklace structure. Due to their index contraction pattern, their leading-order behavior is analogous to that of large-N random matrix models and is associated with a planar graph structure. Within this setting, we identify the emergence of a nontrivial ultraviolet fixed point, reminiscent of mechanisms previously observed in matrix models, and discuss its reliability within the present truncation. The robustness of this fixed point will be further investigated through modified Ward identities, following strategies previously developed in the melonic sector.

We complete the analysis of planar Makeenko–Migdal loop equations in the Lorentz-invariant continuum limit. Using our confining twistor-string representation, we compute the quantum fluctuation determinant, which in Minkowski space reduces to a discrete product of finite-dimensional matrix quadratures. The $\zeta$-regularized weight is independent of winding number $w$. Near the mass shell, the pole singularity is generated by $w \to \infty$, suppressing fluctuation variance as $1/w$. The path integral localizes on the classical trajectory, rendering the pole spectrum and transition residues parametrically exact in the large-winding WKB limit. For the open-string meson sector, we fit 40 observed states across five topological boundary sectors ($h=0, \pm 1, \pm 2$). The holonomy shift $h$ accounts for exact geometric degeneracies between parity families, reproducing mass splittings without phenomenological spin-orbit parameters. Evaluated one-loop residues yield theoretical transition cross-sections capturing heavy-mass quenching and phase-space enhancement for high-spin light states. Applying this framework to the pure Yang–Mills closed string, we demonstrate the dynamical stability of the pure-gauge minimal surface: the conformal Liouville anomaly drives the string strictly to the trigonometric minimum ($q=0$). The complex elliptic geometry analytically collapses, yielding linear Regge trajectories. The translation zero-mode measure dynamically nullifies the transition amplitude of the massless scalar ghost, providing an analytic mechanism for a purely gluonic mass gap. Anchoring parameter-free glueball trajectories to the open-string tension natively recovers the exact L"uscher intercept $\alpha(0)=1/12$, perfectly matching established PDG unassigned isoscalar candidates and large-$N_c$ lattice QCD extrapolations.

We prove a fermionic-bosonic duality relation for the Macdonald index in Argyres-Douglas theories of type $(A_1, D_{2k+1})$, thereby yielding a conjectural fermionic formula due to Andrews et al. Our duality is built upon a new conjugate Bailey pair to be established using techniques from orthogonal polynomials and basic hypergeometric series. In addition, this fermionic formula implies another sum-like expression independently conjectured by Andrews et al. and Kim et al. for the same Macdonald index.

We show that multi-invariants provide necessary and sufficient criteria for full separability in finite-dimensional multipartite systems. For tripartite three-qubit states, the third-order negativity gives an exact criterion for full separability for both pure and mixed states. We then extend the framework to four-qubit pure states, whose full characterization requires eighteen independent real parameters. We identify eighteen independent entanglement measures, consisting of six bipartite, eight tripartite, and four quadripartite measures, with the third-order negativity serving as a key separability criterion. Finally, we generalize the construction to multipartite qudit systems and discuss an application to conformal field theory.

We carry out an “experimental analysis” in which we explicitly compute all possible Abelian two-particle decay channels (excluding the tachyon) of open bosonic massive states up to level (8), amounting to approximately 2,000,000 cases. The aim is to develop intuition about which states are the most stable and to identify the dominant decay channels. Our results show that, for all levels considered, the ratio of decay widths between the slowest- and fastest-decaying states is of order one. In most cases, the dominant polarized decay channel accounts for at least $10\%$ of the total decay width, while the first five channels together contribute roughly 60%. Even when we sum about $10000$ polarized channels. Dominant polarized channels always involve at least one photon and all strings ultimately decay into a photon carrying energy at the string scale. The most stable states are made using the DDF/lightcone oscillators $A_{-1}$ and some $A_{-2}$ and are close relatives of the states on the leading Regge trajectory. Finally, we discuss how the computation on the lightcone differs from the equal-time computation due to “surges”, i.e., decays into a tachyon and a higher-mass state, and we hypothesize that, in bosonic string theory, decays into tachyons constitute the dominant decay channels.

In the framework of the covariant canonical formalism of quadratic gravity, we consider the problem of confinement of massive ghost which violates the unitarity of the physical S-matrix. It is shown that if there is a bound state between the massive ghost and Faddeev-Popov ghost the massive ghost is confined in the zero-norm states through the BRST quartet mechanism, thereby the unitarity being restored. Based on the superfield formulation by Bonora and Tonin, we show that the asymptotic field of the massive ghost must be a massive dipole whereas that of the bound state obeys a massive Klein-Gordon equation. This situation may be of some similarity to color confinement in quantum chromodynamics (QCD) where it is conjectured that not a massless but a massive gluon is in fact confined.

We investigate the pole structure of Kerr black-hole perturbations in the frequency domain, focusing on the building blocks of the Green's function for the radial Teukolsky equation: the homogeneous radial solutions, the connection coefficients, and the Green's function itself. We show that the homogeneous solutions and the local connection coefficients develop simple poles at the Matsubara frequencies, thereby establishing the Matsubara pole structure explicitly within the Teukolsky formalism for asymptotically flat Kerr black holes. At the level of the local fixed-sector connection formula, the explicit Matsubara-pole factors cancel in the ratio of connection coefficients entering a decomposed Green's function contribution. We also identify higher-order zero-frequency singularities in the decomposed Green's function contributions, which scale as $\omega^{-2l-1}$ and cancel collectively in the total radial Green's function. These results clarify how Matsubara poles and sectoral zero-frequency singularities arise in the Teukolsky formalism and provide a frequency-domain foundation for understanding prompt response in time-domain ringdown waveforms in Kerr spacetime.

We reconstruct a static and spherically symmetric black hole geometry originally proposed as an effective metric by identifying a consistent matter source derived from a fundamental action. The space-time is supported by a magnetically charged nonlinear electrodynamics (NED) field non-minimally coupled to a scalar field. Dimensional consistency reduces the parameter space to a single magnetic charge, and the inverse construction formalism yields a one-parameter family of electromagnetic Lagrangians $\mathcal{L}(F)=F^{n+1}/(n+1)$, encompassing both linear and nonlinear electrodynamics. We analyze the horizon structure and determine the critical magnetic charge separating black hole and horizonless configurations. The photon sphere and the corresponding shadow radius are computed, and observational bounds from the Event Horizon Telescope for Sagittarius A* constrain the allowed range of the magnetic charge. In the extended phase space thermodynamics, the solution satisfies the first law and the Smarr relation, exhibits a Hawking-Page phase transition, and presents a single change in stability without van der Waals-type critical behavior. We also investigate the topological properties of both the photon sphere and the thermodynamic parameter space. The photon sphere carries a total topological charge $Q_{\text{tot}}=-1$, while the thermodynamic vector field yields a global winding number $W=0$, placing the solution in the same topological class as the one of the Reissner-Nordström black hole. We finally discuss the versatility of this non-minimal coupling framework in both providing theoretical support to previously introduced solution and also to connect them to observational settings within strong-field gravity.

In non-relativistic mechanics, the total (orbital) angular momentum (AM) of a spatially-distributed system can be decomposed into intrinsic and extrinsic contributions. In relativistic quantum mechanics, intrinsic AM is typically associated with spin, which can be described using the Pauli-Lubanski four-vector. Here, we develop a unified formalism that combines the main features of both approaches and describes the intrinsic AM of a relativistic wavepacket, including both spin and orbital contributions. Our approach is based on the "expectation Pauli-Lubanski vector" constructed from the expectation values of the wavepacket's momentum and AM. Equivalently, it defines the intrinsic AM relative to the wavepacket's energy centroid. In contrast to the conventional Pauli-Lubanski formalism, the zero-mass singularity does not occur for the expectation Pauli-Lubanski vector. Consequently, the intrinsic AM of a wavepacket may have an arbitrary orientation with respect to its momentum, even for massless particles. We illustrate the general theory with a number of examples of relativistic wave beams and packets carrying spin and orbital AM.

We review the status of Birkhoff's theorem in the presence of nonlinear electrodynamics (NLE) - extending the analysis to the case without asymptotic flatness. This leads to the Bertotti-Robinson-type (direct product) geometry with generally unequal radii for its $AdS_{2}$ and $S_{2}$ factors, determined by a given NLE model. As can be expected, such a geometry can also be recovered from a near-horizon limit of the corresponding extremal NLE charged black hole (if it exists). These extremal black holes are shown to be linearly stable for specific NLE models, unlike in the Maxwell-$\Lambda$ case where unequal radii also arise in near-horizon geometry. Regular particle-like models are constructed by replacing the interior of these black holes with corresponding Bertotti-Robinson-type geometry. We also revisit the NLE generalization of the Bonnor-Melvin universe, describing a regular axisymmetric configuration of magnetic field lines in gravito-magnetic equilibrium. Explicit examples are derived for the Maxwell, Born-Infeld, RegMax, and Frolov-Hayward theories of electrodynamics.

Schwarzschild black holes are expected to emerge as the end states of the classical gravitational collapse from non-singular configurations. After integrable curvature singularities appear, the interior geometry can be modelled to exhibit a transition, called “Minkowski breaking”, when the inner horizon disappears, before all matter collapses into the central singularity. This picture implies a quantum framework to describe the final stages of the gravitational collapse, and here we will provide more insights from the semiclassical approximation for the energy-momentum tensor and the Madelung approximation for collapsing matter. In particular, we will show that the quantum potential in the Raychaudhuri equation starts to strongly oppose the collapse towards the Schwarzschild singularity precisely after the Minkowski breaking.

We propose a new “boundary” term in free bosonic string field theory. Here, the term “boundary” refers to a contribution introduced to restore the cyclicity broken by the insertion of a stringy step-function operator, although it is not strictly localized as it involves an operator that selects positive-energy modes. We construct this term as a bilinear form involving the commutator of the BRST operator with the step-function operator. The resulting action has a well-defined variational principle. When evaluated on on-shell string fields, the proposed term reproduces the correct tree-level two-point amplitude for both open and closed strings. We verify this explicitly in the tachyon and massless sectors.

We define a higher-derivative generalization of Maxwell-Chern-Simons theory in $\mathcal{N}=1$ and $\mathcal{N}=2$ superspaces. In particular, the chosen higher-derivative operator is a polynomial function of the d'Alembertian of arbitrary degree, and it is introduced exclusively in the gauge sector. The main goal is to explicitly compute the one-loop quantum corrections to the superfield effective potential for these theories. This is carried out by means of background field quantization in a higher-derivative $R_\xi$ gauge. The effective potential is obtained in closed form and expressed in terms of the roots of polynomial functions.

We present a time-resolved digital quantum simulation of cosmological particle creation in a de~Sitter–radiation FLRW transition. Instead of compiling only the final Bogoliubov transformation into a one-shot circuit, we discretize the conformal-time evolution and implement the dynamics as a Trotterized sequence of short-time circuit blocks. This formulation gives access not only to the late-time particle number, but also to the build-up of fixed-basis pair occupation during the non-adiabatic transition. Using a four-qubit single-excitation encoding for a momentum pair $(+\mathbf{k},-\mathbf{k})$, we compare matrix-Trotter evolution, noiseless statevector simulation, finite-shot Qiskit Aer simulation, and a shallow $N=1$ IBM hardware implementation. The simulator results are consistent with the analytic sudden-transition benchmark $n_k=1/[4(k\eta_e)^4]$ in the controlled single-excitation regime. The IBM experiment demonstrates execution of the shallow circuit block, but exhibits a residual hardware error of order $10^{-2}$, indicating that quantitative hardware reconstruction of the particle spectrum remains beyond current NISQ performance.

We construct a Weyl x SU(2)_L x U(1)_Y invariant theory by extending four-dimensional Weyl quadratic gravity with Weyl-invariant scalar, fermion, Yukawa and gauge sectors. The quadratic structure (R^tilde - mu^2 |phi|^2)^2 allows the Weyl Goldstone mode to be extracted via a Stueckelberg mechanism independent of the Higgs field. Spontaneous breaking of Weyl gauge symmetry reduces the Weyl quadratic curvature to the Einstein-Hilbert action with a positive cosmological constant, generates a mass term for the Weyl gauge field, and simultaneously produces the Higgs potential -mu^2 |phi|^2 + lambda^2 |phi|^4, which is otherwise forbidden by the symmetry. Our framework unifies the Stueckelberg, Higgs and Yukawa mechanisms, reproduces Standard Model mass generation, and predicts additional Higgs-induced contributions to the Weyl gauge field mass, together with a set of Higgs-Weyl couplings. These interactions provide new phenomenological handles, including a vector dark matter candidate, and highlight the geometric origin of mass.