Papers

The Bumblebee gravity (BG) model, featuring spontaneous Lorentz symmetry breaking via a vector field non-minimally coupled to curvature, has been widely used to explore Lorentz-violating effects in cosmology. We investigate primordial black hole (PBH) formation within this framework, deriving the complete set of modified perturbation equations. We demonstrate that BG, sourced by a timelike vector field, introduces three distinct enhancements to PBH abundance–modified expansion history, suppressed collapse threshold, and amplified power spectrum–which together render PBHs viable dark matter candidates across the asteroid-mass window for modest Lorentz-violating couplings. However, a systematic analysis of the quadratic action reveals that these phenomenological consequences emerge from a theoretically pathological foundation. The vector sector exhibits an intrinsic ghost instability, while the requirement of a stable symmetry-breaking minimum simultaneously induces a tachyonic instability on timescales far below cosmological scales. The model thus suffers from a fundamental inconsistency: the conditions for cosmological viability and spontaneous symmetry breaking are mutually exclusive within the minimal Bumblebee framework. Our results illustrate both the notable power of Lorentz violation to influence early Universe observables and the necessity of a consistent theoretical foundation for such predictions.

We obtain an experimental constraint on possible Born-rule violations at high-energy colliders. We model Born-rule violations with differential scattering cross sections $d\sigma/d\Omega$ subject to an angular smearing by a narrow Gaussian of width $\varepsilon$ (with respect to $x=\cos\theta$ for scattering angle $\theta$). For large-angle Bhabha ($e^{+}e^{-} \rightarrow e^{+}e^{-}$) scattering, at a centre-of-mass energy $\sqrt{s}=29\, \mathrm{GeV}$, data from the PEP collider at SLAC allow us to set an upper bound of $\varepsilon<0.042$ at $95\%$ confidence. This corresponds to a Gaussian smearing over an angular range of twice the experimental bin width, and hence provides a physically meaningful limit on deviations from the Born rule. Future prospects for improving this limit are discussed.

We study the error-correcting properties of pure-state holographic geometries, in which mixed boundary subregions are replaced, via the surface/state correspondence, by the Ryu–Takayanagi (RT) geodesic bounding their entanglement wedges. In AdS$_3$/CFT$_2$ we derive a cross-ratio threshold relation $\eta'/\eta = e^{\Delta H/2}$ for the connected/disconnected transition of the entanglement wedge when two holes are punched in such a geometry. The quantity $\Delta H$ is sourced entirely by geodesics ending on RT boundaries. It shifts the standard two-interval threshold $\eta = 1/2$, and we classify when its sign is fixed by the pattern of hole endpoints. Turning to code properties, we show that the recursive hole-punching underlying uberholography cannot start within an RT-boundary, while an untouched asymptotic boundary can still fractalize, and we find numerically that in the configurations we study it does so with the universal fractal dimension $\alpha \approx 0.786$. The resulting upper bounds on price and distance are nevertheless procedure dependent. In the configurations we study, punching holes on the asymptotic boundary while retaining the RT-boundary yields strictly tighter bounds than first tracing out the RT-boundary and then fractalizing.

Motivated by the recent rebuttal of black hole–dark matter solutions based on velocity-matching, we reconstruct the spacetime by treating the dark matter halo density directly as an energy-density source in the Einstein field equations. We obtain an exact static, spherically symmetric black hole solution and investigate the effects of the halo on its geometry, optical properties, quasinormal modes, and thermodynamics. Using null geodesics, we show that the halo modifies photon trajectories, shifts the circular photon orbit, and enlarges the photon sphere and apparent shadow. The Lyapunov exponent of the unstable null orbit further determines the eikonal quasinormal modes, yielding explicit halo-induced corrections to their oscillation and damping rates. We also compute the mass, Hawking temperature, entropy, heat capacity, and Gibbs free energy to characterize the thermodynamic stability and phase structure. We find that the dark matter halo enlarges the domain of thermodynamic stability and introduces nontrivial phase behavior absent in the Schwarzschild case, demonstrating that astrophysical dark matter environments can leave potentially observable imprints on black hole observables.

We study three-dimensional Einstein gravity with negative cosmological constant on non-compact spatial boundaries within the Chern-Simons formulation. Using an exact fluid/gravity correspondence, we derive a closed radial flow equation for the quasi-local stress tensor and show that it realizes the holographic $\sqrt{T\bar T}$ deformation at finite cutoff. We further develop the inverse-scattering description of the boundary dynamics, identifying the gravitational interpretation of the associated spectral data and analyzing the finite-cutoff deformation of soliton solutions. Although the boundary evolution is governed by an integrable bi-Hamiltonian hierarchy, we show that the radial flow itself is not Hamiltonian with respect to the canonical Poisson structure. Our results establish a unified framework connecting integrability, quasi-local gravitational observables, inverse scattering, and finite-cutoff holography on non-compact boundaries.

Higgs Branches of 5d SCFTs are hyperkähler cones, symplectic varieties with interesting nested singularities governing the structure of possible Higgs branch RG flows. The main purpose of this note is to investigate 5d Higgs Branches via a geometric route: we study 5d SCFTs geometrically engineered from M-theory on non-compact Calabi-Yau threefolds, with non-isolated singularities. We match the (dynamical) complex structure deformations of the threefold with the symplectic leaves in the Higgs branch of the 5d SCFT, constructing its stratification purely relying on geometry. Consistency checks for our proposal are presented exploiting magnetic quivers.

We review existing and construct new two-dimensional field theories that exhibit BMS$_3$ symmetry, with and without central extensions. These include interacting electric, magnetic and canonical BMS$_3$ scalar theories, as well as couplings between the electric and magnetic sectors. We provide a careful analysis of boundary contributions at the corner points $u\rightarrow\pm\infty$, determine the counterterms and boundary conditions required by BMS$_3$ invariance, and study the corresponding variational principles. Furthermore, we introduce external sources and derive the associated flux-balance laws. Within the framework of flat-space holography, we show that a simple free electric BMS$_3$ model with the appropriate central charge reproduces the monodromy classification of three-dimensional Einstein gravity. Finally, we investigate the flat-space limits of both AdS$_3$ and dS$_3$, whose boundary dynamics are described by Carrollian limits of Liouville and Euclidean Liouville theory, respectively. Although the resulting BMS$_3$ theories possess isomorphic spectra, they differ in the signs of the supertranslation charges and the central charge. This suggests that the flat-space limits of AdS$_3$ and dS$_3$ provide complementary realizations of flat-space holography.

A new field, Particle Cosmology, emerged at the interface of elementary particle physics and cosmology in the last two decades of the 20th century. In this chapter of the Proceedings of the 4th International Symposium on the History of Particle Physics, the Standard Model and Beyond I will review the development of Particle Cosmology in the period 1980-2000 centered on two events: a conference, Inner-Space/Outer-Space held at Fermilab in May 1984 \cite{kolb1986innerspace} and the 1994 Snowmass Summer Study Particle and Nuclear Astrophysics in the Next Millennium \cite{kolb1995particle}.

The Ding-Iohara-Miki (DIM) algebra (quantum toroidal algebra of $\widehat{gl_1}$) is related to a wide class of quantum many-particle integrable systems, a typical one being the Ruijsenaars trigonometric system with eigenfunctions that are a triad formed by the Noumi-Shiraishi power series, the Macdonald polynomials, and the Baker-Akhiezer multivariable function. Other integrable systems of this type are obtained from the Ruijsenaars system by twisting. At the same time, the Ruijsenaars Hamiltonians are directly related to the Hamiltonians of another quantum integrable system, the Cherednik DAHA Hamiltonians of type $A$ (and their twisted versions in the twisted case), due to the correspondence between the DIM algebra and the spherical DAHA. The eigenfunctions of the DAHA Hamiltonians are non-symmetric Macdonald polynomials. Similarly, there is a class of integrable DAHA Hamiltonians of type $C^\vee C$, the spherical version of which, in turn, allows one to generate integrable Koornwinder Hamiltonians. The eigenfunctions of these two integrable systems are, respectively, non-symmetric and symmetric Koornwinder polynomials, which are our main interest in this paper. Here we consider the cases of both type $A$ and type $C^\vee C$ systems, since they are sufficiently similar, and point out important distinctions between them.

We investigate the Casimir response of a massive scalar field in a torsionless helicoidal spacetime with Levi-Civita connection. The background is ultrastatic and curved, with scalar curvature \(R=-2\Omega^2\), and its off-diagonal metric component induces a geometric coupling between angular and axial quantum numbers. We show that individual modes exhibit a linear helicoidal splitting, whereas the linear contribution cancels in the nonchiral vacuum sum. The leading Casimir correction is therefore quadratic in the twist and defines a helicoidal vacuum susceptibility after local ultraviolet subtractions. For a cylindrical Dirichlet cavity, we compute this scheme-defined susceptibility and the associated correction to the radial Casimir force. The results identify torsionless helicoidal geometry as a controlled setting in which mode-level chirality produces a finite quadratic response of vacuum fluctuations.

While vacuum decay is traditionally described by Euclidean instanton methods, lattice simulations enable real-time modeling of dynamical observables relevant to cosmology and upcoming cold-atom analog experiments. We investigate the relationship between these approaches by extracting ensemble-averaged bubble profiles from zero-temperature simulations of a relativistic scalar field. Our observed profiles differ markedly from the bare Coleman bounce and classical thermal predictions. However, we find that instanton solutions in an appropriately renormalized potential reproduce both the measured profiles and their dependence on the UV cutoff, and predict decay rates consistent with simulations across the parameter range considered. The fact that a single renormalized Euclidean object captures these independent observables provides strong evidence that renormalization accounts for the discrepancy between the two formalisms, and establishes a quantitative link between instanton predictions, lattice simulations, and forthcoming empirical tests of vacuum decay.

Soft de Sitter Effective Theory is a well-motivated candidate for the correct effective late-time description of equal-time correlation functions in de Sitter space. In this work, we study its application to theories that enjoy classical conformal invariance, using the conformally-coupled $\phi^4$-theory as a toy model. While quantum effects generate non-trivial late-time dynamics in such models, we argue that it is not described by the standard construction of the effective theory as discussed thus far in the literature. We show that the tree-level matching of the trispectrum onto the effective theory does not fit into the expected power-counting scheme, and we contrast it with the matching of the tree-level bispectrum in the conformally-coupled $\phi^3$-theory, where it works consistently. We then propose a prescription to identify the leading superhorizon degrees of freedom in such theories, which should serve as the starting point for the construction of their late-time effective description. The interpretation of logarithms of the form $\log(-k\eta)$ in this context is briefly discussed.

Recent studies have identified a new component in black-hole ringdown from merging binaries, termed the direct wave. This component was argued to be tied to the dynamical source evolution near the black-hole horizon, and thus to encode horizon information. Yet a firm theoretical foundation for the direct wave has been lacking. Here we fill this gap by deriving direct waves from first principles in Schwarzschild spacetime, using the causal structure of the Green's function. We show that the direct wave does not vanish and is governed by the near-horizon source dynamics. Our results establish a theoretical basis for direct waves as a probe of near-horizon dynamics, complementary to quasinormal modes.

Wilson loop operators in Chern-Simons theory have revealed profound links between quantum field theory, the fractional quantum Hall effect, topology, conformal field theory, and string theory. In Chern-Simons theories with charge conjugation symmetry, we construct a new class of observables: codimension-two monodromy defects around which fields return to themselves up to charge conjugation. Whereas Wilson loops are labeled by integrable representations of an untwisted affine Lie algebra, monodromy defects are labeled by those of the corresponding twisted affine algebra. The modular and fusion data of these two algebras determine the exact correlation functions of Wilson lines and monodromy defects, which together furnish a $\mathbb{Z}_2$-crossed braided tensor category. The spectrum of line defects in Chern-Simons theory thus gives a physical realization of every algebra in Kac's classification of affine Lie algebras: untwisted for Wilson loops, twisted for monodromy defects. We also determine the exact 't Hooft expansion of monodromy defects in $SU(N)_k$ Chern-Simons theory and identify their holographic duals in topological string theory. The insertion of the lightest monodromy defect has a striking effect: it replaces the resolved conifold background of the Gopakumar-Vafa duality by a specific orientifold of the resolved conifold, transmuting the dual theory of oriented strings into one of unoriented strings. Each excited monodromy defect is then realized as a collection of branes in the orientifold background, with the brane content determined by the representation of the twisted affine algebra that labels the defect.

Quantum anomalies provide a bridge between ultraviolet properties of a theory and its infrared sector. We study how this connection appears in axial-charge-flow observables. In the simplest example, an axial-charge detector probes the fermionic cut of the anomalous triangle and resolves its infrared content as an angular distribution. The massless limit does not commute with the angular integration: a contribution suppressed at fixed angle collapses onto the two beam-collinear directions while retaining the finite integrated sum rule fixed by the axial anomaly. We then replace the axial-charge detector by higher-spin helicity (zilch) detectors and study a family of axial-anomaly-controlled energy-weighted sum rules for the corresponding fluxes. We further show that the same singular localization mechanism and finite zilch-flux sum rules persist in the mixed axial-gravitational channel. We briefly comment on extensions to more general states and multipoint correlators.

We review recent progress in understanding certain aspects of condensed matter systems from a high energy theory perspective. We discuss effective field theories that describe collective bulk and localized excitations in a variety of solid and fluid systems. Particular emphasis is placed on the role played by spacetime symmetries and their spontaneous breaking. The resulting Goldstone dynamics can be seen as underlying a wide variety of phenomena. We attempt to bridge the language gap between subfields while underscoring the numerous conceptual similarities.

Five-dimensional $\mathcal{N}=1$ superconformal field theories admit a rich variety of generalised global symmetries, including higher-form and 2-group symmetries and their 't$~$Hooft anomalies. We show that this data can be extracted directly from the blow-up equations governing the instanton partition functions of such theories on the $\Omega$-background. The central object is the classical prefactor $\exp(-V_n)$ weighting each magnetic flux on the blown-up geometry: evaluated on a background for the electric 1-form symmetry, the fractional parts of its exponents encode the cubic self-anomaly of the 1-form symmetry and its mixed anomalies with the instanton, flavour, gravitational, and $\mathrm{SU}(2)_R$ symmetries. Combined with the faithful continuous global symmetry of the ultraviolet fixed point, determined from the superconformal index, the same data decides whether the theory possesses a 2-group symmetry or a mixed 't$~$Hooft anomaly. We illustrate the method in gauge theories, including $\mathrm{SU}(4)$ and $\mathrm{USp}(4)$ with antisymmetric hypermultiplets and $\mathrm{Spin}(7)$ and $\mathrm{Spin}(8)$ with vector hypermultiplets, as well as in several families of non-Lagrangian theories. New results include the effective prepotentials of the $B_N$ and $B_N^{(1,2,3)}$ families, the cubic 1-form anomalies of the rank-two theories $\mathbb{P}^2\cup\mathbb{F}_3$ and $\mathbb{P}^2\cup\mathbb{F}_6$, and several mixed 1-form–flavour and 1-form–$\mathrm{SU}(2)_R$ anomalies.

Berends–Giele currents have recently attracted renewed attention across the amplitude community, appearing in new contexts ranging from gravitational amplitudes to cosmological correlators and string theory. They can be derived from first principles using the perturbiner method, a thirty-year-old framework that organizes tree-level scattering data in the form of classical multi-particle solutions to field theory equations of motion. After its rediscovery about a decade ago, it has been systematically studied and applied in many different domains. This review aims to provide a pedagogical introduction to the method, covering its basic formulation across a broad but certainly not exhaustive range of models and progressing to some of the most recent findings in the literature. This includes several unpublished results, many of which represent tacit knowledge of the community that has not previously appeared in print.

We derive positivity bounds on the complete dimension-eight effective field theory of photons and a massless dark photon. The mixed gauge sector contains twelve CP-even Wilson coefficients and an enlarged helicity-amplitude structure. Using a modified forward-limit dispersion relation, we analytically obtain non-trivial linear and non-linear elastic positivity constraints that define a spectrahedral geometry. We analyze implications of these bounds on non-forward amplitudes and discuss where kinetic-mixing and dark-axion-portal UV completions populate this geometry.

We study gauge dependence in proper-time renormalisation group flows for asymptotically safe quantum gravity. Working in an essential scheme, we use field redefinitions to separate redundant off-shell contributions from the on-shell running of physical couplings. We consider two approximations: in the first, we work on general backgrounds and project onto all terms with up to four derivatives, neglecting boundary terms; in the second, we work on a maximally symmetric background and retain all orders in the Ricci scalar. Although the flow equation depends on the gauge parameters, this dependence can be cancelled order by order once the redundant terms are absorbed by field redefinitions. In the four-derivative approximation, the dependence on the retained gauge parameter drops out of the beta function for Newton's constant to third order in the coupling. On the sphere, the flow becomes independent of both parameters of the general gauge to all curvature orders, and all orders in the coupling. Crucially, this cancellation depends on the choice of regulator. We verify the mechanism explicitly at one loop, where the gauge-dependent fluctuation contributions are cancelled by the ghost sector on shell. The resulting essential flow displays a gauge-independent non-Gaussian fixed point, supporting the interpretation that universal information in quantum gravity is encoded in the on-shell essential sector.

I construct a microscopic ADHM/chiral-Wishart representative of the reduced charge-sector coefficient $W_\nu[b]$ that enters the Type-IIB axion–dilaton wormhole partition function $Z_{\rm wh}(\theta;b)$. I fix the axion-charge sector, equivalently the form-field-flux sector, which plays the exact same structural role as a fixed-topology sector in QCD: it supplies the domain where I compute the microscopic coefficient before forming the final theta sum. At $E=0$, the axion–dilaton radial family reaches its BPS instanton endpoint. After I impose the Hamiltonian constraint, gauge quotient, charge-sector boundary condition, and collective zero-mode quotient, the physical quadratic fluctuation operator at that endpoint becomes a positive adjoint square. Its non-zero spectrum is therefore a squared singular-value spectrum, and its microscopic endpoint is a Laguerre/chiral hard edge. The D(-1)/D3 super-ADHM collective-coordinate integral supplies the Type-IIB microscopic representative of this same coefficient. In the large$N$ result of Dorey et al., this super-ADHM measure becomes the $k$-D-instanton measure on $AdS_5\times S^5$, multiplied by a centered zero-dimensional supersymmetric matrix-model factor. The chiral/Wishart ensemble forms the hard-edge limit of the rectangular block inside this super-ADHM integral. Fermionic ADHM variables and supergravity fermions remain part of the coefficient: in protected sectors they cancel paired non-zero modes, impose zero-mode saturation, and determine which reduction data \(b\) give a non-vanishing $W_\nu[b]$.

We present a study of Lorentz invariance violation (LIV) in neutrino oscillations, with primary emphasis on the interplay between CPT-violating and CPT-conserving Standard Model Extension (SME) coefficients. We find that $a_{ee}$ and $a_{\tau\tau}$ dominate among the diagonal LIV coefficients, whereas $a_{e\mu}$ and $a_{e\tau}$ provide the most significant off-diagonal contributions. In contrast, the corresponding $c_{\alpha\beta}$ coefficients have comparatively sub-leading effects. Taking DUNE as a representative long-baseline experiment, we show that the sensitivity to CP violation is modified by LIV in a parameter-specific manner. We find correlations between off-diagonal LIV parameters, and non-trivial dependence on the new phases. In absence of LIV, DUNE is expected to establish CP violation at $5\sigma$ for a limited fraction of $\delta_{CP}$ values. We find that the presence of $a_{ee}$, $a_{\tau\tau}$, $a_{e\mu}$ and $a_{e\tau}$ weakens the CP discovery potential, reducing the achievable significance to below $3\sigma$ over a substantial fraction of $\delta_{\rm CP}$. The independent impact of $c_{\alpha\beta}$ terms also results in suppression, but in combination with $a_{\alpha\beta}$, they introduce degeneracies, complicating the extraction of $\delta_{CP}$. This generally results in a deterioration of CP violation sensitivities below $5\sigma$. These findings emphasize the importance of incorporating LIV effects in precision oscillation studies at upcoming long-baseline experiments.

We have investigated a fermionic system from the perspective of an effective quantum field theory defined on a nontrivial topology in the presence of an external magnetic field. Using the proper-time representation, we obtained one-loop expressions for the corresponding effective Lagrangian, taking into account all Landau levels in the propagator. We also computed the significant boundary-induced contributions to the system's magnetization. To verify the reliability of our results, we examined the limit of zero temperature and infinite spatial extent, which correctly reproduces the celebrated Schwinger result.

We study in detail a recent proposal stating that M-theory observables arising from the quantisation of M2-branes are naturally computed in a fixed $A_3$ ensemble. In a holographic setting this implies that in a semiclassical approximation 11d bulk observables in an asymptotically AdS$_4$ background are computed in a grand canonical ensemble of fixed chemical potential $\mu$ conjugate to the integer $N$ determining the rank of the gauge group in the dual CFT. We provide detailed precision tests of holography in the fixed $\mu$ ensemble by focusing on the two leading terms in the derivative expansion of the 11d theory. In addition, we study one-loop logarithmic corrections which we compute in detail. For asymptotically AdS$_4\times S^7/\mathbf{Z}_k$ 11d backgrounds our results are in agreement with supersymmetric localisation calculations in the dual ABJM SCFT. Moreover, we employ the logarithmic corrections in the $\mu$ ensemble to determine the measure of the integral Laplace transform and use this to compute dual SCFT supersymmetric partition functions, like the superconformal index and the squashed $S^3$ partition function, to all orders in the perturbative $1/N$ expansion in terms of Airy functions in harmony with results and conjectures in the dual SCFT.

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we invoke the beauty of the basic canonical (anti)commutators to prove the nilpotency property of the Noether (anti-)BRST charges for the D-dimensional BRST-quantized version of the free Abelian 2-form gauge theory which is endowed with a non-trivial Curci-Ferrari (CF) type restriction. In this proof, we use only the theoretical strength of the Gauss divergence theorem. We demonstrate that, under the off-shell nilpotent (anti-)BRST symmetry transformations, the Noether conserved (anti-)BRST charges are not invariant and they are also found to be not off-shell nilpotent (if we exploit the standard relationship between the continuous symmetry transformations and their generators as the Noether conserved charges). However, these charges become (anti-)BRST invariant and nilpotent if we use (i) the appropriate equations of motion at suitable places, and (ii) the Gauss divergence theorem. We derive the consistently modified versions of the Noether (anti-)BRST charges which are invariant under the off-shell nilpotent (anti-)BRST transformations. We prove the (anti-)BRST invariance of these modified versions of charges by using the basic canonical (anti)commutators, too. We discuss the physicality criteria w.r.t. (i) the conserved Noether (anti-)BRST charges, and (ii) the modified (anti-)BRST invariant versions of the Noether (anti-)BRST charges. We prove the superiority of the latter over the former (in view of the consistency with the Dirac quantization conditions for the gauge theories).

We construct a correspondence between a broad class of unitary matrix models and vacuum correlation functions in quantum spin-chain Hilbert spaces. The key step is to lift symmetric functions to operators acting on the $N$-magnon sector in a way that preserves the relevant ring structure. For any unitary matrix model whose integrand admits a factorized expansion in symmetric functions, the Schur orthogonality of the unitary group integral is then translated into the inner product of quantized Schur states. We illustrate the construction for the Gross–Witten–Wadia model, superconformal indices of $\mathcal{N}=4$ super Yang–Mills theory with classical gauge groups, and Toda tau functions. The resulting operator formulation provides a unified algebraic bridge between unitary matrix integrals, quantum integrable systems and symmetric function theory.

Mathematicians have embraced interactive theorem provers with growing enthusiasm – building large shared libraries and machine-checking a string of landmark results. Theoretical physics is different: most of its results are not theorems but justified by arguments the community trusts without a rigorous proof. For many – the one we treat here among them – no rigorous proof is within reach. For 4d Yang–Mills theory, deriving exact rigorous results from first principles would first require constructing the interacting theory nonperturbatively, which is a sizable piece of one of the Clay Millennium prize problems. We argue here that an interactive theorem prover can be used to verify some non-rigorous physics arguments. The method is to postulate a short list of explicit, named physical postulates, which imply the physical results by virtue of a machine-checkable proof. The trust that remains then rests on that short, inspectable list, and the prover can report, for any downstream result, exactly which assumptions it used. We carry this out for the Seiberg–Witten solution of ${N}=2$ $SU(2)$ super-Yang–Mills – the genus-one case – formalized in Lean 4; the higher-genus $SU(N)$ generalization is developed in the same repository as an axiomatized skeleton and left to future work. We describe what is proved, what is assumed, how the assumptions are checked – external review and an independent numerical oracle – and why this discipline is a sound standard for validating AI-generated results in theoretical physics. What we offer is a discipline, reviewable on its own terms: a reader may take the Seiberg–Witten mathematics on trust and still assess the formalization method.

An intermediate scale R-axion faces an immediate obstruction from the Dine-Festuccia-Komargodski (DFK) bound on the superpotential, $2|\langle W\rangle|\leq f_R F$, since for a nearly Minkowski vacuum it typically follows that $f_R\gtrsim M_{\rm Pl}$. We show that this lower bound on $f_R$ can be relaxed in an effective construction with the scalar potential tuned near zero via a mixed $F$- and $D$-term uplift, leading to a metastable vacuum in which the usual Planckian-$f_R$ inference from the DFK argument is avoided locally. Validity of the effective field theory and metastability of the small $f_R$ vacuum generically both imply a relaxed bound: $ f_R \gtrsim \sqrt{m_{3/2}M_{\rm Pl}} $. We also highlight that if the R-symmetry has a QCD anomaly, this potentially permits the R-axion to play the role of the QCD axion. TeV-scale supersymmetry permits $f_R\sim10^{11}$ GeV, this not only evades certain astrophysical and cosmological axion constraints, but notably lies in the window for which the observed dark matter abundance can be reproduced by the R-axion via the misalignment mechanism.

We discuss a recent proposal for constructing “syzygy solutions”, which play a crucial role in integration-by-parts reductions for multi-loop scattering amplitudes. We highlight a relationship between syzygies and the leading Landau singularities of Feynman diagrams and discuss how this implies that integral relations are controlled by infrared singularities. We use this insight to systematically construct highly compact, determinantal syzygy solutions, providing an explicit, simple example at one loop. We demonstrate the power of this approach by applying it to a two-loop pentabox family relevant for the NNLO corrections to $pp \rightarrow t\overline{t}H$ at the LHC.

We nonperturbatively compute Rényi entropies for strip-shaped subregions in the three-dimensional O(4) model at finite density on the lattice. By using a dual variable representation and a tailored worm algorithm, we circumvent the sign problem when sampling the grand canonical ensemble. In the limit of large subregions, we also establish a direct, quantitative relationship between the derivative of entanglement entropy with respect to the size of the entangling region and the thermal entropy density for general quantum field theories, providing a new way to study their thermodynamics. We corroborate this argument with our lattice results by demonstrating that, in the appropriate limit, the derivative of entanglement entropy satisfies the same Maxwell relation as the thermal entropy density.