We present a new bound for the worldvolume actions of branes with a Wess-Zumino term. For this we introduce a generalization of calibrations for which the calibration form is not closed. We then apply our construction to find the M-5-brane worldvolume solitons in an AdS background that saturate this bound. We show that…
The paper proves a Hawking-type singularity theorem using worldvolume quantum strong energy inequalities.
problem Improving classical singularity theorems with weakened energy conditions.
method Integral Ricci curvature bounds based on worldvolume quantum strong energy inequalities.
result Past geodesic incompleteness proven in cosmological scenarios.
Unified description of string and brane worldvolumes using auto-parallel vector fields.
problem Describing worldvolumes of strings and branes in arbitrary backgrounds.
method Introducing auto-parallel generalised vector fields and their properties.
result Unified worldvolume equations for strings and branes.
M5-branes' flux quantization linked to non-abelian cohomology.
problem Flux quantization on M5-branes and its implications.
method Analogous to Dirac's charge/flux quantization, constraining M5's flux-quantization law to non-abelian cohomology theory.
result Skyrmion-like and anyonic solitons on M5-branes and open M5-branes.
Researchers create holographic super-embeddings for M5 and M2 branes.
problem No concrete examples of super-embeddings for M5 and M2 branes existed.
method Constructed explicit holographic super-embeddings of probe M5 and M2 branes into their super-AdS backgrounds.
result Explicit holographic super-embeddings of M5 and M2 branes were successfully constructed.
Constructs brane current algebras from QP-manifolds, generalizing string currents.
problem Constructing brane current algebras from QP-manifolds.
method Using Poisson algebra and QP-manifolds (symplectic L∞-algebroids), the paper derives a universal geometric form for Poisson brackets of brane currents. result Derives a universal expression for 't Hooft anomaly in the presence of fluxes.
Cohomotopy charge quantization implies String structure on M5-branes.
problem Charge quantization in M-theory.
method J-twisted Cohomotopy and higher Sp(1)-gauge field analysis.
result Emergence of twisted String structure on M5-branes.
The actions, anomalies, and quantization conditions allow the M2-brane and the M5-brane to support, in a natural way, structures beyond Spin on their worldvolumes. The main examples are twisted String structures. This also extends to twisted String^c structures, which we introduce and relate to twisted String structure…
M-theory can be defined on closed manifolds as well as on manifolds with boundary. As an extension, we show that manifolds with corners appear naturally in M-theory. We illustrate this with four situations: The lift to bounding twelve dimensions of M-theory on Anti de Sitter spaces, ten-dimensional heterotic string the…
Modernizes higher-dimensional supergravity, linking it to flux quantization.
problem Constructing infrared completions of higher-dimensional supergravity.
method Using differential nonabelian cohomology and super-torsion constraints.
result Equivalence of solutions in different dimensions and flux quantization.
Proves Hawking's theorem for less smooth spacetime metrics.
problem Proving Hawking's singularity theorem for less smooth spacetime metrics.
method New estimates for Ricci curvature and a segment-type inequality for volume control.
result Proves Hawking's singularity theorem for Lipschitz metrics.
We develop an approach to Khovanov homology of knots via gauge theory (previous physics-based approches involved other descriptions of the relevant spaces of BPS states). The starting point is a system of D3-branes ending on an NS5-brane with a nonzero theta-angle. On the one hand, this system can be related to a Chern…
We explain how, starting with a stack of D4-branes ending on an NS5-brane in type IIA string theory, one can, via T-duality and the topological-holomorphic nature of the relevant worldvolume theories, relate (i) the lattice models realized by Costello's 4d Chern-Simons theory, (ii) links in 3d analytically-continued Ch…
The paper explores how fields in higher dimensions are quantized.
problem Understanding non-perturbative completions of higher gauge fields.
method Generalizes the Chern-Dold character map to higher-dimensional supergravity theories.
result Flux and charge quantization laws for higher gauge fields are understood via non-linear Bianchi identities.
New mathematical framework connects M-theory charges to stable homotopy groups.
problem Quantization of fluxes in M-theory and their mathematical representation.
method Establishing a correspondence between M-theory phenomena and stable homotopy theory concepts.
result Found a direct link between M-theory charges and stable homotopy groups.
The goal of this paper is to re-examine D-brane Ramond-Ramond field couplings in the presence of a B-field. We will argue that the generalised geometry induced on the world volume by the B-field results in an important but subtle change on the coupling. In order to explain this, we use the language of differential K-th…
We consider an open string version of the topological twist previously proposed for sigma-models with G2 target spaces. We determine the cohomology of open strings states and relate these to geometric deformations of calibrated submanifolds and to flat or anti-self-dual connections on such submanifolds. On associative …
The worldvolume theory of coincident M5-branes is expected to contain a nonabelian 2-form/nonabelian gerbe gauge theory that is a higher analog of self-dual Yang-Mills theory. But the precise details -- in particular the global moduli / instanton / magnetic charge structure -- have remained elusive. Here we deduce from…
Unified Higgs bundle vacua from M-theory on Spin(7) spaces.
problem Unifying Higgs bundle vacua from different string compactifications.
method Developed formalism for M-theory on local Spin(7) spaces and constructed explicit solutions.
result Unified 3D effective field theory from 4D M- and F-theory vacua.
We consider SU(2)-equivariant dimensional reduction of Yang-Mills theory on manifolds of the form M×S3/Γ, where M is a smooth manifold and S3/Γ is a three-dimensional Sasaki-Einstein orbifold. We obtain new quiver gauge theories on M whose quiver bundles are based on the affine ADE Dynkin diagram associ…
The recently conjectured knots-quivers correspondence relates gauge theoretic invariants of a knot K in the 3-sphere to representation theory of a quiver QK associated to the knot. In this paper we provide geometric and physical contexts for this conjecture within the framework of the large N duality of Ooguri…
We formalize higher dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory (the true home of the "FDA"-language used in the supergravity literature). We show generally how the intersection laws for s…
We uncover and highlight relations between the M-branes in M-theory and various topological invariants: the Hopf invariant over Q, Z and Z2, the Kervaire invariant, the f-invariant, and the ν-invariant. This requires either a framing or a corner structure. The canonical framing pro…
We explore 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at θ=π (SU(2)θ=π YM), by turning on backg…
The study optimizes bounds for comparing training and population loss.
problem Optimizing bounds for comparing training and population loss.
method Derives generic information-theoretic and PAC-Bayesian generalization bounds using convex comparator functions.
result The tightest possible bound is obtained with the comparator being the convex conjugate of the CGF of the bounding distribution.
Introduces bounded scale measure and generalizes property A.
problem Defining property A for large scale spaces with bounded geometry.
method Introduces bounded scale measure, shows its coarse invariance, and generalizes property A.
result Definition of property A for large scale spaces with bounded scale measure is a coarse invariant.
Paper improves PAC-Bayes bounds for various loss types.
problem Improving PAC-Bayes bounds for different types of losses.
method Introducing new high-probability PAC-Bayes bounds for bounded and general tail behaviors losses, and extending to anytime-valid bounds.
result New fast-rate and mixed-rate bounds for losses with bounded ranges, and parameter-free bounds for losses with general tail behaviors.
Improved bounds for Monte Carlo Rademacher Averages using self-bounding functions.
problem Proving sharper concentration bounds for MCERA.
method Deriving new bounds through self-bounding functions and concentration of measure.
result Novel bounds depend on data-dependent quantities, improving over standard methods.
Study bounds on self-shrinkers with bounded HA for applications.
problem Understanding bounds on self-shrinkers with bounded HA.
method Integral and pointwise bounds on the second fundamental form of self-shrinkers.
result Gap and compactness results for self-shrinkers.
Investigates tight PAC-Bayes bounds for small datasets.
problem Tightening PAC-Bayes bounds for small data.
method Generic PAC-Bayes theorem, meta-learning, synthetic tasks.
result PAC-Bayes bounds are competitive with Chernoff bounds but not as tight.
Extends Fatou theorem to bounded harmonic maps.
problem Classical Fatou theorem for bounded harmonic functions.
method Extending theorem to bounded harmonic maps.
result Identifies bounded harmonic maps on unit disk with bounded measurable functions on boundary.
New bound relaxes uniform gradient norm assumptions for PAC-Bayesian bounds.
problem Generalization bounds with strict assumptions like uniformly bounded loss.
method Relax uniform bounds assumptions to on-average bounded loss and gradient norm.
result Proposes a new generalization bound with a surrogate of model complexity.
Jiang et al. (2020) found no uniformly tight generalization bounds for neural networks in the overparameterized setting.
problem Finding uniformly tight generalization bounds for neural networks in the overparameterized setting.
method Examined more than a dozen generalization bounds, proving that no bounds can be uniformly tight in the overparameterized setting.
result No generalization bounds can be uniformly tight in the overparameterized setting.
Willmore-type inequalities for bounded domains in manifolds with curvature bounds.
problem Establishing inequalities for bounded domains in manifolds with curvature bounds.
method Using asymptotic or integral Ricci curvature bounds to establish inequalities.
result Recovering a recent inequality of Jin-Yin.
Lower bounds on curvature integral for manifolds with curvature constraints.
problem Bounding curvature integrals under curvature constraints.
method Proving a lower bound for the curvature integral using dimension, upper curvature bounds, and injectivity radius.
result Uniformly bounded below integral of scalar curvature.
Paper improves SLCB regret bound for bounded noise.
problem Stochastic linear contextual bandits with bounded noise.
method Set-membership estimation (SME) and optimism in the face of uncertainty (OFU).
result Improved regret bound of O(logT). Study on CMC hypersurfaces with bounded index and area, proving multiplicity one convergence and bounds on genus.
problem Understanding CMC hypersurfaces with bounded index and area.
method Bubble-compactness theory for embedded CMC hypersurfaces in low dimensions.
result Minimal blow-ups are all catenoids, and bounds on genus provided.
Uniform entropy bound for Ricci shrinkers with bounded curvature.
problem Bounding entropy for Ricci shrinkers with specific curvature constraints.
method Establishing uniform entropy bounds for simply connected Ricci shrinkers with a finite second homotopy group and uniform curvature bounds.
result Uniform entropy bound for simply connected Ricci shrinkers with a finite second homotopy group and uniform curvature bounds.
New study on regret lower bounds for multi-agent multi-armed bandit problems.
problem Understanding the limits of performance in multi-agent multi-armed bandit problems.
method Comprehensive study on different settings, establishing tight lower bounds.
result First comprehensive study on regret lower bounds across various settings.
The paper improves PAC-Bayes bounds for losses with finite moments.
problem Bounding generalization for losses with heavy tails and finite moments.
method Truncation method and PAC-Bayes bounds for unbounded losses with heavy tails and bounded variance.
result Bounds interpolate between slow and fast rates depending on the moment.
Sharp lower bound for Hodge Laplacian on Kähler hyperbolic manifolds.
problem Finding a sharp lower bound for the spectrum of the Hodge Laplacian.
method Explicitly expressed in terms of the supremum norm of the 1-form.
result Explicit spectral lower bounds for bounded symmetric domains.
New bounds for SGD show improved performance in various settings.
problem Improving convergence bounds for SGD with random permutations.
method Analyzing convergence of SGD with random reshuffling and arbitrary permutations.
result Tighter lower bounds for weighted average iterates in both convex and strongly-convex cases.
Uniform bounds for eigenvalues of Hodge Laplacian on manifolds with lower Ricci curvature.
problem Establishing bounds for eigenvalues of Hodge Laplacian under lower Ricci curvature.
method Using geometric assumptions including lower Ricci curvature, injectivity radius, and diameter bounds.
result Uniform eigenvalue bounds for the Hodge Laplacian and connection Laplacian.
The paper honors Lai's contributions to multi-armed bandits and establishes new regret bounds.
problem Improving regret bounds in multi-armed bandit problems.
method Establishes non-asymptotic regret bounds for upper confidence bound indices.
result New regret bounds match Lai-Robbins lower bound.
New method to parametrize infinite Riemann surfaces with bounded triangulations.
problem Parametrizing infinite Riemann surfaces with bounded triangulations.
method Introducing bounded ideal triangulations and proving real-analyticity of the parametrization.
result Real-analytic parametrization of Teichmüller spaces for infinite surfaces with bounded triangulations.
We propose a general framework for studying adaptive regret bounds in the online learning framework, including model selection bounds and data-dependent bounds. Given a data- or model-dependent bound we ask, "Does there exist some algorithm achieving this bound?" We show that modifications to recently introduced sequen…
Triangulates surfaces with bounded energy using diffeomorphisms.
problem Triangulating surfaces with bounded Kolasinski--Menger energy.
method Uses bounded distortion diffeomorphisms of subsets of a plane.
result Triangulation with bounded number of triangles.
This paper analyzes regret bounds for Gaussian process Thompson sampling.
problem Analyzing the performance of Gaussian process Thompson sampling (GP-TS) in Bayesian optimization.
method The paper derives several regret bounds for GP-TS, including a lower bound, upper bounds on the second moment of cumulative regret, expected lenient regret, and improved cumulative regret.
result The paper provides improved regret upper bounds for GP-TS, showing that it suffers from a polynomial dependence on 1/δ with probability δ.