Papers

Our recent result on the construction of perfect fluid equations with N=1,2 Schrödinger supersymmetry [Mod. Phys. Lett. A 41 (2026) 2550214] is extended to accommodate nonrelativistic conformal supersymmetries of other types. Two cases are considered in detail, which include the N=2 conformal Newton-Hooke superalgebra and N=1 l-conformal Galilei superalgebra with arbitrary half-integer parameter l. Supersymmetric fluid models are built within the Hamiltonian framework by introducing real (for N=1) or complex (for N=2) anticommuting field variables as superpartners for the density and velocity. For both the cases the full set of conserved charges associated with the superalgebras is constructed and the Lagrangian description is given. Subtleties with the construction of perfect fluid equations with N=2 l-conformal Galilei supersymmetry are discussed as well.

Using holographic duality, we reveal a transition in vortex dipole dynamics below a critical dipole size in strongly interacting superfluids, characterized by a significant suppression of mutual friction. In the bulk, this transition is triggered by a topological reconnection of vortex tubes, which disconnects the boundary vortices from the black hole horizon and forms a U-pipe. Consequently, the post-transition evolution is governed by the contraction of the bulk U-pipe rather than the mutual friction associated with the horizon, revealing a scale-dependent dissipation mechanism. We further show that this reconnection persists over a broad temperature range, even when the transition becomes unobservable at high temperatures. Our results provide a dissipation-based interpretation for the anomalous critical dipole scale observed in strongly interacting cold-atom experiments, and suggest the existence of distinct dissipative regimes in strongly interacting superfluids.

The gradient expansion and the separate universe approach provide an effective description of inflationary soft modes after coarse-graining shorter-wavelength degrees of freedom. We formulate a locality condition on the quantum state, requiring that the hard-mode state in each local universe depend on the soft modes only through the local soft-mode values in the same patch. When this condition is satisfied, the coarse-grained soft-mode dynamics remains local, and loop corrections from hard modes to superhorizon correlators of the adiabatic curvature perturbation are perturbatively suppressed. This provides a model-independent diagnosis of when enhanced corrections due to hard modes can invalidate the gradient expansion. We further show that the same locality condition implies a generalized soft theorem, from which the standard consistency relations follow under additional assumptions. This formulation clarifies the origin of possible deviations from the standard consistency relations in multi-field systems or in a non-attractor background. We also show that the locality condition guarantees the absence of infrared divergences for the correlators of operators invariant under a large gauge transformation. Thus, locality of the hard-mode state provides a unified criterion for the effective description of inflationary soft modes, generalized soft theorems, the suppression of hard-mode loop corrections, and the infrared regularity of observable correlators.

We extend our previous analysis [Phys. Rev. D 109, 065005 (2024)] of CPT-odd electromagnetic response in tilted, anisotropic Weyl semimetals to the overtilted (type-II) regime, where electron and hole pockets coexist at the Fermi level. Starting from the minimal QED sector of the Standard-Model Extension matched to a lattice-motivated anisotropic Dirac Hamiltonian with tilt, we compute the zero-temperature finite-density effective action nonperturbatively from the vacuum polarization tensor, and corroborate the result using a complementary chiral kinetic theory formulation that consistently incorporates both Fermi-sea and Fermi-surface contributions. In the type-II regime the unbounded linear dispersion necessitates a physical ultraviolet regularization. Implementing a hard momentum cutoff tied to the lattice bandwidth, we show that the CPT-odd, axion-like response remains finite across the type-I to type-II Lifshitz transition, while acquiring tilt- and anisotropy-dependent renormalizations together with nonuniversal, cutoff-sensitive terms governed by the geometry of the electron and hole pockets. As a concrete application, we evaluate the anomalous Hall conductivity in the prototypical type-II Weyl semimetal WTe$_2$, using parameters extracted from first-principles calculations and experiments, and find that Fermi-sea and Fermi-surface contributions are comparable and partially cancel, yielding a finite and strongly anisotropic Hall response characteristic of the overtilted regime.

We investigate thick-brane configurations in five-dimensional $f(T,T_G)$ modified teleparallel gravity. In five dimensions, the torsional Gauss-Bonnet invariant $T_G$ contributes dynamically, leading to genuinely new effects even at linear order. Within a warped geometry supported by a scalar field, we construct explicit solutions and show that the $T_G$ sector significantly modifies the brane structure. In particular, the coupling parameter controls the deformation of the warp factor and energy density, allowing for the emergence of brane splitting and nontrivial internal structure. We further analyze the localization of spin-$1/2$ fermions via a Yukawa coupling. The system admits a normalizable chiral zero mode, while the opposite chirality remains delocalized. The massive Kaluza-Klein spectrum is strongly affected by the torsional Gauss-Bonnet term, which modifies the effective potentials and leads to the appearance of resonant quasi-localized states.Our results show that $f(T,T_G)$ gravity provides a richer framework for braneworld models, where torsional higher-order corrections play a key role in shaping both geometry and field localization.

All standard scalar quantum-information measures – concurrence, negativity, entanglement entropy, the optimized CHSH bound, and quantum Fisher information – are CP-blind in ideal \\ spin-0 $\to f\bar f$ decays because the two-qubit spin state is maximally entangled for every CP angle. We show that stabilizer magic, fixed in the physical Pauli frame of spin analysis, escapes this blind spot: the stabilizer Rényi entropy admits an exact closed form, vanishing at CP-definite and Clifford phases and peaking at maximal non-Clifford mixing. Two experimentally accessible, magic-inspired CP witnesses follow; the linear amplitude is $14.3\times$ more efficient than its quartic counterpart and reaches discovery-level sensitivity at the HL-LHC for $H\to\tau^+\tau^-$.

We develop an operator-algebraic framework for modular self-duality, symmetrized relative entropy, and Bogoliubov–Kubo–Mori (BKM) susceptibility of local states in quantum field theory. In finite dimensions, modular self-duality singles out fixed points at which a state coincides with its modularly reflected partner. At such points, the natural comparison functional is the symmetrized Umegaki relative entropy. It vanishes at coincidence, and its Hessian is governed by the BKM quantum Fisher information along the reflected tangent direction. We then extend this fixed-point construction to the local type~III von Neumann algebras that arise in quantum field theory. Here, a local state is compared with the modular pullback of its commutant restriction, and the intrinsic comparison functional is the symmetrized Araki relative entropy. For sufficiently regular state deformations, the fixed-localization Hessian at the self-dual point defines a type~III BKM susceptibility. This coefficient is obtained by evaluating the BKM bilinear form on the tangent selected by the modular pairing. Exact coherent-state realizations are obtained for the free scalar field on wedge algebras and for the chiral $U(1)$ current on half-line algebras. In both examples, the comparison functional is exactly quadratic in the deformation parameter, and the susceptibility coefficients admit explicit boost-energy, stress-tensor, or half-line integral representations. We also apply the construction to a ball-shaped boundary region in the vacuum state of a conformal field theory with a semiclassical anti-de Sitter (AdS) gravitational dual. For linear bulk coherent excitations in an exact complementary-recovery model of this sector, bulk–boundary modular intertwining identifies the modular partner with the AdS–Rindler-reflected coherent state, and the symmetrized relative entropy is exactly quadratic.

There exist only four known string theories with minimal supersymmetry in eight dimensions, whose low energy effective descriptions are given by minimal supergravity coupled to $l=18$, $10$, or $2$ vector multiplets. It has been argued that these numbers are uniquely fixed by consistency conditions of the effective theory. In this work, we investigate the protected couplings of minimal supergravity coupled to two vector multiplets under the assumption that the theory admits a duality symmetry of the form $\Gamma_0(N)\times \Gamma_0(N)\subset {\rm SL}(2,\mathbb{Z}) \times {\rm SL}(2,\mathbb{Z})$ for some positive integer $N$. We show that consistency with anomaly cancellation, higher-dimensional uplifts, and gauge enhancement loci strongly constrains the allowed couplings and isolates a unique consistent theory in the BPS sector. In particular, we find that the Bianchi identity for the three-form flux cannot have gravitational contributions.

We study the late-time behaviour of nonlinear perturbations of Schwarzschild-AdS$_4$ black branes and show that real-analytic initial data generically enter a regime controlled by the large-$k$ tail of the quasinormal mode spectrum $\{\omega_{k\,n}\}$. Using the asymptotic scaling $\mathrm{Im}\,\omega_{k\,n} \sim k^{-1/5}$ of the planar AdS$_4$ black brane, we derive a universal prediction that boundary observables decay in a stretched-exponential manner, specifically as $\exp(-c\, t^{5/6})$ up to a mild polynomial prefactor. Fully nonlinear numerical evolutions employing Fourier spectral and discontinuous Galerkin methods confirm this behaviour for small black holes and show consistent scaling - after suppressing long-lived low-$k$ modes - for larger ones. These results indicate that stretched-exponential decay with exponent $5/6$ is a robust feature of AdS$_4$ gravitational dynamics with real-analytic data, arising from geometric-optics physics rather than hydrodynamic modes.

A central open problem in quantum gravity is to understand how continuum spacetime emerges from quantum-geometric degrees of freedom in a background-independent setting. A many-body perspective suggests that spacetime emerges as a hydrodynamic phase of many atoms of quantum geometry. This idea underlies several approaches to quantum gravity, and it has been explicitly realised in the group field theory formalism. However, quantum fluctuations beyond the mean-field regime remain largely unexplored. We fill this gap by importing Bogolyubov theory to quantum gravity condensates, showing that leading beyond-mean-field effects manifest as collective excitations, in direct analogy with phonons in laboratory BECs. We implement the construction in a tractable group field theory model, where condensates of quantum-geometric atoms reproduce nonsingular expanding cosmologies, and derive the leading beyond-mean-field corrections to the emergent Friedmann dynamics. These results identify a new class of quantum-gravity excitations and establish a controlled bridge between microscopic quantum-gravitational dynamics, many-body collective phenomena, and signatures of spacetime emergence.

We analyse two static spacetimes, recently generated from a Schwarzschild–Bertotti–Robinson electrovacuum seed through distinct symmetry transformations. The electromagnetic field of the transformed solutions can be set to zero and both solutions were presented as vacuum solutions of General Relativity. However, we show that once recast in Weyl form, both metrics are seen to be supported by a semi-infinite annular mass distribution on the equatorial plane. Thus, these metrics harbour a hidden matter source, visible in Weyl coordinates. In the original Schwarzschild-like coordinates equatorial null geodesics reach spatial infinity ($r\to\infty$) in finite affine parameter. In the Weyl representation, these geodesics approach the inner edge of the annulus, where the coordinate map degenerates.

We study the relation between geodesic completeness, the averaged null energy condition (ANEC), and spatial curvature in Friedmann–Robertson–Walker (FRW) cosmology within classical general relativity. Using the affinely parameterized ANEC along radial null geodesics, we prove that non-static flat or open FRW spacetimes in the regular classes considered here cannot be both null geodesically complete and ANEC-satisfying. Bounded oscillatory or cyclic flat/open models do not circumvent the obstruction: the negative affine-ANEC bulk term accumulates over infinitely many cycles, giving \(I_{\rm ANEC}=-\infty\) for non-static periodic cases. Equivalently, within these classes, non-static ANEC-satisfying flat or open models are null incomplete. The sign obstruction is absent in closed \((k=+1)\) FRW geometry, where the positive curvature term enters the affine ANEC identity with the opposite sign and can support nonsingular, geodesically complete cosmologies with ordinary NEC-respecting matter. We give explicit closed-FRW scalar-field constructions, including a fully analytic quadratic reconstruction and a cubic-root reconstruction in closed quadrature, and contrast them with their flat realizations, which require NEC-violating support. Furthermore, we quantify how positive curvature can bias flat-model reconstructions toward an effective phantom equation of state, finding only a percent-level effect under current curvature bounds. The result is a curvature classification of ANEC-compatible eternal FRW cosmology: flat and open branches are obstructed, while the closed branch admits explicit complete realizations, with global de Sitter appearing as the vacuum limiting representative.

We review well known classical energy conditions and their implications for gravitational solutions, including the celebrated Hawking and Penrose singularity theorems. We then consider quantum fields coupled to gravity, where the topic becomes both richer and more subtle, as even the simplest quantum theories violate local energy conditions. We discuss directions for constraining energy densities in quantum field theories, including averaging over regions of spacetime and bounds relating energy and quantum information. We explore implications of these bounds for quantum field theory coupled to gravity as an effective theory and discuss how they guide our understanding of quantum gravity more broadly. These notes are based on a series of lectures given at the XXI Modave Summer School in Mathematical Sciences.

The absence of global symmetries in a quantum gravity theory often requires the introduction of (new) symmetry-breaking defects, which appear as singular objects in the low-energy description. This has been formalized in the Cobordism Conjecture, which further relates the asymptotics of these defects to non-trivial deformation classes of the effective theory. In this work we investigate the symmetry-breaking defects for theories with a discrete symmetry $G$ encoded in the bordism groups $\Omega^{\xi}_2 (BG)$ and, in particular, its sub-class described in terms of the homology groups $H_2(BG;\mathbb{Z})$. Contrary to expectations we find that the defects are naturally described in terms of networks of codimension-two objects rather than isolated objects in codimension three. While in special situations linking configurations of defects are sufficient, our strategy generically predicts the existence of junctions, thus suggesting an extended applicability of the Cobordism Conjecture. We demonstrate the viability of this approach in four-dimensional supergravity theories originating from string and M-theory with a discrete Heisenberg group acting on its axionic degrees of freedom.

Proca and Maxwell fields in $d$-dimensional Schwarzschild black holes with anti-de Sitter (AdS) asymptotics are investigated through their linear perturbations and associated quasinormal modes (QNMs) with Dirichlet boundary conditions at infinity. The Proca field equations reduce to one decoupled and two coupled radial wave-like equations. We demonstrate how the Maxwell equations emerge from the zero-mass limit of the Proca system. Several analytical properties of the corresponding QNM spectrum are examined. To compute the QNM frequencies, we employ two complementary numerical methods particularly suited to asymptotically AdS spacetimes. Using these techniques, we determine the QNMs modes of Proca field perturbations in $4$, $5$, $6$, and $7$-dimensional Schwarzschild-AdS backgrounds. As a new result, we find numerically that scalar-type Maxwell perturbations in large $d\geq 5$ Schwarzschild-AdS black holes exhibit purely imaginary low-frequency modes, analogous to those found in vector-type gravitational perturbations. The presence of such modes is especially relevant within the AdS/CFT correspondence, as they correspond to the linearized hydrodynamic regime in the dual conformal field theory. We also analyze the influence of the Proca mass on the QNM spectrum, also emphasizing how Maxwell modes are recovered in the massless limit. The dependence of the spectrum on the black hole radius is explored. In addition, analytic expressions for the QNM frequencies of vector-type and monopole Proca perturbations, as well as Maxwell modes, are derived for small $d$-dimensional Schwarzschild-AdS black holes by matching asymptotic expansions using an intermediate region. These analytic results show good agreement with the numerical findings, confirming, in particular, the existence of purely imaginary low-frequency scalar-type Maxwell modes in large $d\geq 5$ Schwarzschild-AdS spacetimes.

We present a non-perturbative method through which local probes can access the two-point function of a quantum field within a region of spacetime. By considering a lattice of gapless particle detectors, we identified the probe observables that encode the field's two-point function. We quantify the discrepancies introduced by physical finite-sized interaction regions by performing a spacetime multipole expansion of the smeared two-point function. Our protocol expresses the two-point function entirely in terms of measurable detectors correlations, providing an operational notion of states in QFT.

We propose a covariant holographic c-function, defined directly in a top-down background and constructed from the extrinsic curvature of codimension-two slices of the bulk geometry. The definition does not rely on a special choice of coordinates or on the existence of a consistent dimensional reduction. We show that it unifies previous foliation-based holographic c-functions into a single covariant formula, reducing to them in the appropriate limits. We evaluate the covariant expression in a range of top-down string backgrounds, including conformal models, confining geometries, flows across dimensions, and the Klebanov-Murugan geometry, in which the holographic radial direction mixes with internal coordinates and which is not the uplift of a lower-dimensional solution. In all cases, the c-function behaves as expected: it interpolates monotonically between AdS fixed points when they are present and decreases towards zero in gapped infrared regions, while in the Klebanov-Murugan case we recover the correct fixed-point values and find evidence for monotonicity. We highlight open conceptual issues, including: the lack of a universal covariant definition of the holographic radial direction in the presence of a nontrivial internal manifold; the derivation of the flow from a bulk action; and the relation to the entanglement c-function.

We investigate the emergence of random-matrix statistics in the D1D5 CFT by studying second-order lifting matrices in low-energy near-BPS sectors. We compare the $N=3$ finite-$N$ lifting problems with the planar large-$N$ limit at fixed orbifold conformal weight and R charges. In the planar large-$N$ limit at fixed orbifold energy, mixing between single-cycle and multi-cycle states is suppressed, and the symmetry-resolved lifting spectra display Poisson-like level statistics. At finite $N$, non-planar terms restore this mixing between different cycle structures. Within the resulting symmetry-resolved sectors, this finite-$N$ mixing is accompanied by level repulsion consistent with random-matrix behavior. These results suggest that, in the low-energy near-BPS sectors accessible to our analysis, non-planar cycle-structure mixing at finite $N$ is associated with the onset of level repulsion and random-matrix-like spacing statistics.

The general idea of this paper is to start from a classical integrable (partial differential) equation which arises as a compatibility condition for a matrix linear differential problem. For definitiveness' sake, a generalised sinh-Gordon equation depending on $2N-1$ complex coefficients or moduli is considered. Then, the connexion coefficients (Wronskians) of different solutions to this problem satisfy, in the spirit of the Ordinary Differential Equation/Integrable Model correspondence, functional relations, which can be considered, – if supplemented by suitable asymptotic behaviours –, as identifying a specific state of a quantum integrable model: in fact they are the eigenvalues of extensions of Baxter operators $Q$ and $T$, the transfer matrix. Moreover, Y-system and (implementing the asymptotic conditions) thermodynamic Bethe Ansatz equations originate from them, without any passage through the scattering theory, and providing an invariant parametrisation of the monodromy space. The crucial novelty is the modification of all the relations because of their dependence on the moduli. For zero momentum, they fully describe physically the quantum homogeneous sine-Gordon model, i.e. scattering amplitudes of gauge fields in $\mathcal{N} = 4$ SYM at strong coupling or their dual null polygonal light-like Wilson loops in $AdS_3$. As a direct consequence of the correspondence, two Zamolodchikov's conjectures, based on previous results, are also proven.

The Reeh-Schlieder theorem says that every target vector can be approximated from the vacuum by an operator localized in an arbitrarily small spacetime region, but it gives no quantitative cost for doing so. This note isolates a standard Tomita-Takesaki estimate as a model-independent preparation bound. Targets with deeply negative modular energy require large local operators. After rescaling such an operator to a physical contraction, the same estimate becomes a lower bound on postselection overhead. In geometries where the modular Hamiltonian is known, the bound becomes explicit. Bisognano-Wichmann turns it into a boost energy statement for wedges, and the Casini-Huerta-Myers formula gives a stress-tensor version for bounded regions of conformal field theories. Local unitaries can only reach states of nonnegative modular energy. Negative modular sectors require nonunitary or postselected outcomes, giving a preparation cost bound that complements vacuum embezzlement in type III local algebras.

We propose a reformulation of the conformal perturbation theory of the correlation functions in $J\bar{J}$-deformed CFTs as a dressing on the deformed operators, that matches both bare and renormalized perturbation theory. The key is to use the Riemann bilinear identity to convert the deformation into a dressing and a large-cycle integral for higher genus. Based on the proposal, we calculate the deformation of partition functions on the torus and higher genus Riemann surfaces, which can be written as kernel integrals that preserve modular invariance or covariance. We also calculate the flow of the conformal weights and conserved charges along the deformation. Based on this flow and the modular $S$-transformation, we propose a criterion for constructing dressed operators. We test our formalism and results by studying the $O(2, 2)$ theories and strings on the TsT background.

We investigate field theory models of holographic superconductors in which the condensation of the order parameter is induced by a Robin boundary condition. Assuming large-$c$ factorization, we study the phase diagram of a two-dimensional CFT deformed by a relevant double-trace perturbation. Using modular invariance, we relate the high- and low-temperature phases, reproducing analytically the results for the zero-winding sector of the holographic model. Moreover, we match the near-critical behaviour of the condensate with an effective Ginzburg–Landau field theory description. Another important feature of the holographic superconductor is the presence of vortices that carry fractional magnetic flux. We investigate a field theory toy model with similar properties and interpret it as a fractional Little–Parks effect.

We study the near-kernel sector of the Hamiltonian constraint operator in the one-vertex model of quantum reduced loop gravity using variational Monte Carlo methods with neural quantum states. The analysis is based on the symmetric Hamiltonian containing both Euclidean and Lorentzian contributions, and on the variational minimization of the positive quadratic operator $\hat{\mathcal Q}=\hat C \hat C^\dagger$ in truncated Hilbert spaces with spin cutoff up to $j_{\mathrm{max}}=1001$. The resulting near-kernel states are found to organize into three qualitatively distinct classes. At low cutoffs, we find solutions that do not factorize across the three edge degrees of freedom. At larger cutoffs, we find two different factorized branches, both described to very high accuracy by products of one-edge wavefunctions but localized in different spin regimes. One of these branches is matched with near-unit fidelity by reduced Thiemann coherent states, providing evidence for an emergent semiclassical organization of the near-kernel sector. The other is likewise strongly factorized, but its one-edge factors are not well described by the same coherent-state family.

We investigate Krylov spread complexity for the ground state of two-band Hamiltonians, where the reference state is a generic state on the Bloch sphere. The spread complexity is obtained by using a purely geometric formulation in terms of Bloch sphere data without constructing the circuit Hamiltonian. For generic reference states, the derivative of the spread complexity is logarithmically divergent at the topological phase transition in the Su-Schrieffer-Heeger (SSH) model. We demonstrate that the derivative of the spread complexity is bounded by fidelity susceptibility for general two-band models, indicating the sensitivity of the spread complexity to any gap closing (topological or trivial). This is illustrated in the massive Dirac Hamiltonian with a trivial gap closing. Finally, we introduce a non-unitary duality in the SSH model between the topological and trivial phases, which manifests itself in the spread complexity and fidelity susceptibility.

We develop a geometric realization of a broad class of generalized black hole entropy functionals by establishing their direct correspondence with the Misner$-$Sharp quasilocal mass and the Wald Noether$-$charge entropy in scalar$-$tensor theories of gravity. The resulting models feature a scale-dependent effective gravitational coupling, whose functional dependence is determined by the underlying entropy parameters. Within this framework, we derive explicit Einstein-frame scalar potentials: for Barrow entropy, a steep exponential potential; for Tsallis$-$Cirto entropy, an exponential potential governed by the nonextensivity parameter; and for quantum-gravity and entanglement$-$induced corrections, an approximately linear potential. These distinct potentials generate characteristic cosmological phenomenology, with implications for inflationary dynamics, late-time dark-energy behavior, and non-singular bouncing cosmologies. The framework is compatible with current constraints from solar-system tests, big-bang nucleosynthesis, and pulsar-timing observations, and it yields predictions that can be probed by forthcoming observational surveys. In this way, the analysis establishes a unified and geometrically grounded connection between information$-$theoretic entropy proposals and gravitational field theory.

We compute the gravitational impulse for two classical massive scalars in the ultrarelativistic limit to all orders in Newton's constant $G_N$ at fixed $G_N s/m b$ to $O(m^4/s^2)$. By computing the 4 and 5-point scattering amplitudes in the small-mass regime of $-t\sim m^2$, we are able to resum all large $G_N s$ corrections. Applying the KMOC formula for the impulse and taking the large mass limit, we recover the classical result at high energies. This resummation is in complete agreement with known results in the post-Minkowski expansion, and in the massless limit we recover previous results for the radiated energy. We use this resummed amplitude to predict the leading high-energy behavior of the PM expansion to eleventh post-Minkowski order.

The Large Vector Multiple (LVM) is the relevant gauge multiplet for gauging isometries acting on both the chiral and the twisted chiral fields in a $(2, 2)$ sigma model. Here we show that a recently proposed new gauge multiplet is a constrained or partially dualized version of the LVM. Gauging using this multiplet results in a $(2, 2)$ $\beta\gamma$ system interacting with a sigma model.

We present exact expressions, based on the grade restriction rule and window categories, for monodromies associated to certain Calabi-Yau threefold flops. We show a general formula for the monodromy action on the lattice of B-brane charges, based on the hemisphere partition function for abelian and nonabelian gauged linear sigma models. We exploit the explicit form of the discriminant in the quantum Kähler moduli to further refine the form of the monodromies, in several examples, using their relation to the fundamental group of nested torus links.

Low-energy effective theories provide a natural description of four-dimensional physics in higher-dimensional geometries, where the imprint of the bulk geometry appears as parameters of the lower-dimensional theory. Inspired by the Damour-Esposito-Farése (DEF) model of spontaneous scalarization in first generation Scalar-Tensor theories of gravity, we investigate the possibility of tachyonic instability and spontaneous scalarization in braneworld scenarios. We consider the two-brane Randall-Sundrum model where the low-energy effective theory on either brane is of scalar-tensor nature with the extra-dimensional radion playing the role of the scalar. We have determined the possibilities for tachyonic (in)stability of the radion field on either brane in three scenarios: the Randall-Sundrum (RS) model with fine-tuning conditions in which the potential of the radion field vanishes identically, the RS model without fine-tunings where the radion potential arises purely from the gravity sector and the RS model with a bulk stabilizing field that generates a radion potential with a minimum. With the bulk stabilizing field, we have found that on-brane matter with $T>0$ changes the VEV of the radion, destroying the resolution of the gauge hierarchy problem, whereas on-brane matter with $T<0$ does not alter the stability and VEV of the radion. We further determined the exact condition of tachyonic (in)stability of radion field with the on-brane dS$_4$ and AdS$_4$ geometries.

We compute the gravitational form factors (GFFs) of the pion and kaon using their light-front wave functions within the Basis Light-Front Quantization framework. The wave functions are obtained by solving a light-front effective Hamiltonian that incorporates three-dimensional confinement along with a color-singlet Nambu–Jona-Lasinio interaction between the constituent quark and antiquark. The form factor $A(Q^2)$ is found to be in overall agreement with recent lattice QCD and dispersive results. In contrast, $D(Q^2)$ is enhanced in magnitude at low $Q^2$ relative to both lattice QCD and dispersive determinations. This behavior arises from extracting the $D$-term using transverse components of the QCD energy–momentum tensor, which are more sensitive to the small-$x$ region and to light-front zero-mode effects in the present truncated framework. Using the resulting GFFs, we determine the mass (matter) and mechanical radii of the pion and kaon and analyze their mechanical structure through the corresponding pressure and shear-force distributions.