We introduce a general framework for constructing dispersion relations using crossing-symmetric variables, leading to infinitely many distinct representations of the 2-to-2 scattering amplitude of identical scalars. Classical formulations such as the Auberson-Khuri crossing-symmetric dispersion relations (CSDRs), the Mahoux-Roy-Wanders relations, and the local CSDR, as well as fixed-t dispersion relations emerge as special cases. Within this setting we re-derive the null constraints from a geometric perspective. Finally, we present, for the first time, an explicit extension of Roy-like equations that remain valid at arbitrarily high energies, relying only on the rigorously established analyticity domain of scattering amplitudes.

Quantum mechanical lattice models with local, bounded interactions obey Lieb-Robinson causality. We show that this implies a domain of analyticity of the retarded Green's function $G^R(\omega,{\bf k})$ of local lattice operators as a function of complex frequency $\omega$ and momentum ${\bf k}$, similar to the lightcone analyticity property of relativistic field theories. Low-energy effective descriptions of the dynamics must be consistent with this microscopic analyticity constraint. We consider two canonical low-energy fermionic Green's functions describing non-Fermi liquids, the marginal Fermi liquid and the `Hertz liquid'. The pole in these Green's functions must be outside of the Lieb-Robinson domain of analyticity for all complex momenta captured by the low-energy theory. We show that this constraint upper bounds the magnitude of the dimensionless non-Fermi liquid coupling in certain Hertz liquids. We furthermore obtain, from causality, an upper bound on the magnitude $|G^R(\omega,{\bf k})|$ within the analytic domain. We use this bound to constrain the quasiparticle residue of the non-Fermi liquids.

The Drude-Kadanoff-Martin model is a simple low energy and long wavelength description of charge transport, parameterised by the current relaxation timescale $\tau$, charge diffusivity $D$ and charge compressibility $\chi$. We obtain sharp constraints on these parameters in terms of the microscopic energy and length scales of any underlying lattice model with local and bounded interactions. Our primary tools are upper bounds on the retarded Green's function for the charge density in such a setting. We first note that the Drude-Kadanoff-Martin model cannot pertain at microscopic energy scales because it is inconsistent with the exponential suppression of spectral weight at the highest frequencies in a lattice model. Secondly, under the assumption that the low energy dynamics is captured by the model, we obtain a lower bound on the collective mean free path $\ell \equiv \sqrt{\tau D}$. This bound is shown to imply a version of the Mott-Ioffe-Regel bound: systems with $\ell$ much shorter than the lattice length scale cannot have conventional Drude peaks.

The Cosmological Principle (CP) -- the notion that the Universe is spatially isotropic and homogeneous on large scales -- underlies a century of progress in cosmology. It is conventionally formulated through the Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmologies as the spacetime metric, and culminates in the successful and highly predictive $\Lambda$-Cold-Dark-Matter ($\Lambda$CDM) model. Yet, tensions have emerged within the $\Lambda$CDM model, most notably a statistically significant discrepancy in the value of the Hubble constant, $H_0$. Since the notion of cosmic expansion determined by a single parameter is intimately tied to the CP, implications of the $H_0$ tension may extend beyond $\Lambda$CDM to the CP itself. This review surveys current observational hints for deviations from the expectations of the CP, highlighting synergies and disagreements that warrant further study. Setting aside the debate about individual large structures, potential deviations from the CP include variations of cosmological parameters on the sky, discrepancies in the cosmic dipoles, and mysterious alignments in quasar polarizations and galaxy spins. While it is possible that a host of observational systematics are impacting results, it is equally plausible that precision cosmology may have outgrown the FLRW paradigm, an extremely pragmatic but non-fundamental symmetry assumption.

Theories with pseudoscalars that couple through anomalies (such as axion models) are of particular phenomenological interest. We carry out a comprehensive analysis of all bounds obtainable from bootstrapping the amplitudes when a pseudoscalar couples to photons and gravitons. This allows us to find new cutoff scales of theories with anomalies that are more restrictive than those obtained from naive perturbative analysis. Our results are especially relevant for holographic models, as the bounds determine the allowed region of the five-dimensional EFTs, for example, by imposing strong bounds on Chern-Simons terms. We also consider modifications of General Relativity in photon--graviton couplings and show that current experiments are sensitive to these effects only if new physics appears at $\sim 10^{-10}$ eV.

Foundation models are highly versatile neural-network architectures capable of processing different data types, such as text and images, and generalizing across various tasks like classification and generation. Inspired by this success, we propose Foundation Neural-Network Quantum States (FNQS) as an integrated paradigm for studying quantum many-body systems. FNQS leverage key principles of foundation models to define variational wave functions based on a single, versatile architecture that processes multimodal inputs, including spin configurations and Hamiltonian physical couplings. Unlike specialized architectures tailored for individual Hamiltonians, FNQS can generalize to physical Hamiltonians beyond those encountered during training, offering a unified framework adaptable to various quantum systems and tasks. FNQS enable the efficient estimation of quantities that are traditionally challenging or computationally intensive to calculate using conventional methods, particularly disorder-averaged observables. Furthermore, the fidelity susceptibility can be easily obtained to uncover quantum phase transitions without prior knowledge of order parameters. These pretrained models can be efficiently fine-tuned for specific quantum systems. The architectures trained in this paper are publicly available at this https URL, along with examples for implementing these neural networks in NetKet.

The near horizon limit of the extremal BTZ black hole is a``self-dual orbifold'' of AdS_3. This geometry has a null circle on its boundary, and thus the dual field theory is a Discrete Light Cone Quantized (DLCQ) two dimensional CFT. The same geometry can be compactified to two dimensions giving AdS_2 with a constant electric field. The kinematics of the DLCQ show that in a consistent quantum theory of gravity in these backgrounds there can be no dynamics in AdS_2, which is consistent with older ideas about instabilities in this space. We show how the necessary boundary conditions eliminating AdS_2 fluctuations can be implemented, leaving one copy of a Virasoro algebra as the asymptotic symmetry group. Our considerations clarify some aspects of the chiral CFTs appearing in proposed dual descriptions of the near-horizon degrees of freedom of extremal black holes.

The main objective of this work is to isolate Effective Field Theory scattering amplitudes in the space of non-perturbative two-to-two amplitudes, using the S-matrix Bootstrap. We do so by introducing the notion of Effective Field Theory cutoff in the S-matrix Bootstrap approach. We introduce a number of novel numerical techniques and improvements both for the primal and the linearized dual approach. We perform a detailed comparison of the full unitarity bounds with those obtained using positivity and linearized unitarity. Moreover, we discuss the notion of Spin-Zero and UV dominance along the boundary of the allowed amplitude space by introducing suitable observables. Finally, we show that this construction also leads to novel bounds on operators of dimension less than or equal to six.

We explore the spacetime structure near non-extremal horizons in any spacetime dimension greater than two and discover a wealth of novel results: 1. Different boundary conditions are specified by a functional of the dynamical variables, describing inequivalent interactions at the horizon with a thermal bath. 2. The near horizon algebra of a set of boundary conditions, labeled by a parameter $s$, is given by the semi-direct sum of diffeomorphisms at the horizon with "spin-$s$ supertranslations". For $s=1$ we obtain the first explicit near horizon realization of the Bondi-Metzner-Sachs algebra. 3. For another choice, we find a non-linear extension of the Heisenberg algebra, generalizing recent results in three spacetime dimensions. This algebra allows to recover the aforementioned (linear) ones as composites. 4. These examples allow to equip not only black holes, but also cosmological horizons with soft hair. We also discuss implications of soft hair for black hole thermodynamics and entropy.

We investigate the two-dimensional frustrated quantum Heisenberg model with bond disorder on nearest-neighbor couplings using the recently introduced Foundation Neural-Network Quantum States framework, which enables accurate and efficient computation of disorder-averaged observables with a single variational optimization. Simulations on large lattices reveal an extended region of the phase diagram where long-range magnetic order vanishes in the thermodynamic limit, while the overlap order parameter, which characterizes quantum spin glass states, remains finite. These findings, supported by a semiclassical analysis based on a large-spin expansion, provide compelling evidence that the spin glass phase is stable against quantum fluctuations, unlike the classical case where it disappears at any finite temperature.

Theories with pseudoscalars that couple through anomalies (such as axion models) are of particular phenomenological interest. We carry out a comprehensive analysis of all bounds obtainable from bootstrapping the amplitudes when a pseudoscalar couples to photons and gravitons. This allows us to find new cutoff scales of theories with anomalies that are more restrictive than those obtained from naive perturbative analysis. Our results are especially relevant for holographic models, as the bounds determine the allowed region of the five-dimensional EFTs, for example, by imposing strong bounds on Chern-Simons terms. We also consider modifications of General Relativity in photon--graviton couplings and show that current experiments are sensitive to these effects only if new physics appears at $\sim 10^{-10}$ eV.

We introduce a general framework for constructing dispersion relations using crossing-symmetric variables, leading to infinitely many distinct representations of the 2-to-2 scattering amplitude of identical scalars. Classical formulations such as the Auberson-Khuri crossing-symmetric dispersion relations (CSDRs), the Mahoux-Roy-Wanders relations, and the local CSDR, as well as fixed-t dispersion relations emerge as special cases. Within this setting we re-derive the null constraints from a geometric perspective. Finally, we present, for the first time, an explicit extension of Roy-like equations that remain valid at arbitrarily high energies, relying only on the rigorously established analyticity domain of scattering amplitudes.

Expanding around null hypersurfaces, such as generic Kerr black hole horizons, using co-rotating Kruskal-Israel-like coordinates we study the associated surface charges, their symmetries and the corresponding phase space within Einstein gravity. Our surface charges are not integrable in general. Their integrable part generates an algebra including superrotations and a BMS_3-type algebra that we dub "T-Witt algebra". The non-integrable part accounts for the flux passing through the null hypersurface. We put our results in the context of earlier constructions of near horizon symmetries, soft hair and of the program to semi-classically identify Kerr black hole microstates.

We recently reported new results on the $\gamma^{(*)} + N(940)\frac{1}{2}^+ \to \Delta(1700)\frac{3}{2}^{-}$ transition form factors using a symmetry-preserving treatment of a vector$\,\otimes\,$vector contact interaction (SCI) within a coupled formalism based on the Dyson-Schwinger, Bethe-Salpeter, and Faddeev equations. In this work, we extend our investigation to the $\gamma^{(*)} + N(940)\frac{1}{2}^+ \to N(1520)\frac{3}{2}^{-}$ transition. Our computed transition form factors show reasonable agreement with experimental data at large photon virtualities. However, deviations emerge at low $Q^2$, where experimental results exhibit a sharper variation than theoretical predictions. This discrepancy is expected, as these continuum QCD analyses account only for the quark-core of baryons, while low photon virtualities are dominated by meson cloud effects. We anticipate that these analytical predictions, based on the simplified SCI framework, will serve as a valuable benchmark for more refined studies and QCD-based truncations that incorporate quark angular momentum and the contributions of scalar and vector diquarks.

Hamiltonian Truncation (HT) methods provide a powerful numerical approach for investigating strongly coupled QFTs. In this work, we develop HT techniques to analyse a specific Renormalization Group (RG) flow recently proposed in Refs. [1, 3]. These studies put forward Ginzburg-Landau descriptions for the conformal minimal models $M(3,10)$ and $M(3,8)$, as well as the RG flow connecting them. Specifically, the RG-flow is defined by deforming the $M(3,10)$ with the relevant primary operator $\phi_{1,7}$ (whose indices denote its position in the Kac table), yielding $M(3,10)+ \phi_{1,7}$. From the perspective of HT, realising such an RG-flow presents significant challenges, as the $\phi_{1,7}$ deformation requires renormalizing the UV theory up to third order in the coupling constant of the deformation. In this study, we carry out the necessary calculations to formulate HT for this theory and numerically investigate the spectrum of $M(3,10)+ \phi_{1,7}$ in the large coupling regime, finding strong evidence in favour of the proposed flow.

We present a classical kinetically constrained model of interacting particles on a triangular ladder, which displays diffusion and jamming and can be treated by means of a classical-quantum mapping. Interpreted as a theory of interacting fermions, the diffusion coefficient is the inverse of the effective mass of the quasiparticles which can be computed using mean-field theory. At a critical density \r{ho} = 2/3, the model undergoes a dynamical phase transition in which exponentially many configurations become jammed while others remain diffusive. The model can be generalized to two dimensions.

We investigate symmetry and causality constraints on interacting Fermi liquids. Whereas Galilean or Lorentz boost symmetry leads to a well-known constraint on the first Landau parameter $F_1$, we show that scale invariance similarly constrains $F_0$. In the case of conformal Fermi liquids, we show that causality constraints on the particle-hole continuum and on zero sound strongly restrict the available parameter space for interacting Fermi liquids. We also consider nonlinear response, which we show is sensitive to additional ``generalized Landau parameters'' even at lowest orders in the long wavelength limit. We impose Galilean, Lorentz and scale symmetry on these generalized Landau parameters, obtaining further nonlinear constraints. We test our constraints in several microscopic models that enter a Fermi liquid phase.

We revisit the subtelties of computing the high temperature spin stiffness $D$ of the spin-$1/2$ XXZ chain using exact diagonalization to analyze its dependence on system symmetries and ensemble. Within the canonical ensemble and for states with zero magnetization, we find $D$ vanishes exactly due to spin-inversion symmetry for all but the anisotropies $\tilde \Delta_{MN} = \cos(\pi M /N)$ with N > M and coprime, provided system sizes $L \ge 2N$, for which states with different spin-inversion signature become degenerate due to the underlying $sl_2$ loop algebra symmetry. All these loop-algebra degenerate states carry finite currents which we conjecture [based on $L$ and anisotropies $\tilde \Delta_{MN}$ (with $N

We investigate the emergence of a structure in the correlation matrix of assets' returns as the time-horizon over which returns are computed increases from the minutes to the daily scale. We analyze data from different stock markets (New York, Paris, London, Milano) and with different methods. Result crucially depends on whether the data is restricted to the ``internal'' dynamics of the market, where the ``center of mass'' motion (the market mode) is removed or not. If the market mode is not removed, we find that the structure emerges, as the time-horizon increases, from splitting a single large cluster. In NYSE we find that when the market mode is removed, the structure of correlation at the daily scale is already well defined at the 5 minutes time-horizon, and this structure accounts for 80 % of the classification of stocks in economic sectors. Similar results, though less sharp, are found for the other markets. We also find that the structure of correlations in the overnight returns is markedly different from that of intraday activity.