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A bstract We develop an effective field theory for dissipative fluids which governs the dynamics of long-lived gapless modes associated with conserved quantities. The resulting theory gives a path integral formulation of fluctuating hydrodynamics which systematically incorporates nonlinear interactions of noises. The dynamical variables are mappings between a “fluid spacetime” and the physical spacetime and an essential aspect of our formulation is to identify the appropriate symmetries in the fluid spacetime. The theory applies to nonlinear disturbances around a general density matrix. For a thermal density matrix, we require an additional Z 2 symmetry, to which we refer as the local KMS condition. This leads to the standard constraints of hydrodynamics, as well as a nonlinear generalization of the Onsager relations. It also leads to an emergent supersymmetry in the classical statistical regime, and a higher derivative deformation of supersymmetry in the full quantum regime.

Abstract We derive explicit formulae to compute the a and c central charges of four dimensional N 𝓝 = 2 superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of N 𝓝 = 2 SCFTs which culminate with our N 𝓝 = 2 UV-IR simple flavor condition. This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d N 𝓝 = 2 SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper. This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world.

Abstract We study the scalar curvature R of the vector moduli space of 5d𝓝=1supergravities, obtained by compactifying M-theory on a Calabi-Yau three-fold. We find that R can only diverge at points where some gauge interactions go to infinite coupling in Planck units and become SCFTs or LSTs decoupled from gravity and other vector multiplets. For 5d SCFTs of rank r ≤ 2 divergences occur if, additionally, the SCFT still couples to the vevs of such vector multiplets, so that along its Coulomb branch its gauge kinetic matrix and/or string tensions depend on some non-dynamical parameters. If the strong coupling singularity is better understood as a 6d (1, 0) SCFT, as in some decompactification limits, then divergences in R arise when the SCFT is endowed with a non-Abelian gauge group.

A bstract We examine universal positivity constraints on 2 → 2 scattering in 4d planar N = 4 supersymmetric Yang-Mills theory with higher-derivative corrections. We present numerical evidence that the convex region of allowed Wilson coefficients (the “EFT-hedron”) flattens completely along about one-third of its dimensions when an increasing number of constraints on the spectral density from crossing-symmetry are included. Our analysis relies on the formulation of the positivity constraints as a linear optimization problem, which we implement using two numerical solvers, SDPB and CPLEX. Motivated by the flattening, we propose a novel partially resummed low-energy expansion of the 2 → 2 amplitude. As part of the analysis, we provide additional evidence in favor of the conjecture [ 1 ] that the Veneziano amplitude is the only amplitude compatible with both S-matrix bootstrap constraints and string monodromy.

We bootstrap the Veneziano superstring amplitude in 10 dimensions from the bottom-up. Starting with the most general maximally supersymmetric Yang-Mills EFT, we input information about the lowest-lying massive states, which we assume contribute via tree-level exchanges to the 4-point amplitude. We show the following: (1) if there is only a single state at the lowest mass, it must be a scalar. (2) Assuming a string-inspired gap between the mass of this scalar and any other massive states, the allowed region of Wilson coefficients has a new sharp corner where the Veneziano amplitude is located. (3) Upon fixing the next massive state to be a vector, the EFT bounds have a one-parameter family of corners; these would correspond to models with linear Regge trajectories of varying slopes, one of which is the open superstring. (4) When the ratio between the massive scalar coupling and the trF4 coefficient is fixed to its string value, the spin and mass of the second massive state is determined by the bootstrap and the Veneziano amplitude is isolated on a small island in parameter space. Finally, we compare with other recent bootstraps approaches, both the pion model and imposing Regge-inspired maximal spin constraints.

A bstract We propose Swampland constraints on consistent 5-dimensional N = 1 supergravity theories. We focus on a special class of BPS magnetic monopole strings which arise in gravitational theories. The central charges and the levels of current algebras of 2d CFTs on these strings can be calculated by anomaly inflow mechanism and used to provide constraints on the low-energy particle spectrum and the effective action of the 5d supergravity based on unitarity of the worldsheet CFT. In M-theory, where these theories are realized by compactification on Calabi-Yau 3-folds, the special monopole strings arise from wrapped M5-branes on special (“semi-ample”) 4-cycles in the threefold. We identify various necessary geometric conditions for such cycles to lead to requisite BPS strings and translate these into constraints on the low-energy theories of gravity. These and other geometric conditions, some of which can be related to unitarity constraints on the monopole worldsheet, are additional candidates for Swampland constraints on 5-dimensional N = 1 supergravity theories.

A bstract The quiver Yangian, an infinite-dimensional algebra introduced recently in [ 1 ], is the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We introduce trigonometric and elliptic analogues of quiver Yangians, which we call toroidal quiver algebras and elliptic quiver algebras, respectively. We construct the representations of the shifted toroidal and elliptic algebras in terms of the statistical model of crystal melting. We also derive the algebras and their representations from equivariant localization of three-dimensional N = 2 supersymmetric quiver gauge theories, and their dimensionally-reduced counterparts. The analysis of supersymmetric gauge theories suggests that there exist even richer classes of algebras associated with higher-genus Riemann surfaces and generalized cohomology theories.

A bstract Swampland criteria like the Weak Gravity Conjecture should not only apply to particles, but also to other lower-codimension charged objects in 4d EFTs like strings and membranes. However, the description of the latter is in general subtle due to their large backreaction effects. In the context of 4d N = 1 EFTs, we consider 1 2 BPS strings and membranes which are fundamental, in the sense that they cannot be resolved within the EFT regime. We argue that, if interpreted from the EFT viewpoint, the 4d backreaction of these objects translates into a classical RG flow of their couplings. Constraints on the UV charges and tensions get then translated to constraints on the axionic kinetic terms and scalar potential of the EFT. This uncovers new relations among the Swampland Conjectures, which become interconnected by the physical properties of low-codimension objects. In particular, using that string RG flows describe infinite field distance limits, we show that the WGC for strings implies the Swampland Distance Conjecture. Similarly, WGC-saturating membranes generate a scalar potential satisfying the de Sitter Conjecture.

A bstract We bootstrap the Veneziano superstring amplitude in 10 dimensions from the bottom-up. Starting with the most general maximally supersymmetric Yang-Mills EFT, we input information about the lowest-lying massive states, which we assume contribute via tree-level exchanges to the 4-point amplitude. We show the following: (1) if there is only a single state at the lowest mass, it must be a scalar. (2) Assuming a string-inspired gap between the mass of this scalar and any other massive states, the allowed region of Wilson coefficients has a new sharp corner where the Veneziano amplitude is located. (3) Upon fixing the next massive state to be a vector, the EFT bounds have a one-parameter family of corners; these would correspond to models with linear Regge trajectories of varying slopes, one of which is the open superstring. (4) When the ratio between the massive scalar coupling and the tr F 4 coefficient is fixed to its string value, the spin and mass of the second massive state is determined by the bootstrap and the Veneziano amplitude is isolated on a small island in parameter space. Finally, we compare with other recent bootstraps approaches, both the pion model and imposing Regge-inspired maximal spin constraints.

A bstract We study d -dimensional Conformal Field Theories (CFTs) on the cylinder, S d − 1 × ℝ , and its deformations. In d = 2 the Casimir energy (i.e. the vacuum energy) is universal and is related to the central charge c . In d = 4 the vacuum energy depends on the regularization scheme and has no intrinsic value. We show that this property extends to infinitesimally deformed cylinders and support this conclusion with a holographic check. However, for N = 1 supersymmetric CFTs, a natural analog of the Casimir energy turns out to be scheme independent and thus intrinsic. We give two proofs of this result. We compute the Casimir energy for such theories by reducing to a problem in supersymmetric quantum mechanics. For the round cylinder the vacuum energy is proportional to a + 3 c . We also compute the dependence of the Casimir energy on the squashing parameter of the cylinder. Finally, we revisit the problem of supersymmetric regularization of the path integral on Hopf surfaces.