arXiv research

5D gauge theories are dual to 3D and 2D models via Floer homologies.

We show that the smooth geometry of a hyperbolic 3-manifold emerges from a classical spin system defined on a 2d discrete lattice, and moreover show that the process of this "dimensional oxidation" is equivalent with the dimensional reduction of a supersymmetric gauge theory from 4d to 3d. More concretely, we propose a…

Study of 2d gauged linear sigma models to derive difference equations and spectral data.

2d GLSM connects Berry connections to Coulomb branch via difference equations.

The standard Feynman diagrammatic approach to quantum field theories assumes that perturbation theory approximates the full quantum theory at small coupling even when a mathematically rigorous construction of the latter is absent. On the other hand, two-dimensional Yang-Mills theory is a rare (if not the only) example …

We prove that Wilson loop expectation values for arbitrary simple closed contours obey an area law up to second order in perturbative two-dimensional Yang-Mills theory. Our analysis occurs within a general family of axial-like gauges, which include and interpolate between holomorphic gauge and the Wu-Mandelstam-Liebran…

Study of surface defects in gauge theories leads to duality and separation of variables.

We study 4d superconformal indices for a large class of N=1 superconformal quiver gauge theories realized combinatorially as a bipartite graph or a set of "zig-zag paths" on a two-dimensional torus T^2. An exchange of loops, which we call a "double Yang-Baxter move", gives the Seiberg duality of the gauge theory, and t…

Novel $A_{\infty}$-categories derived from gauge theories for manifold homologies.

We consider Chern-Simons theory on 3-manifold $M$ that is the total space of a circle bundle over a 2d base $Σ$. We show that this theory is equivalent to a new 2d TQFT on the base, which we call Caloron BF theory, that can be obtained by an appropriate type of push-forward. This is a gauge theory on a bundle with stru…

We reformulate the compatibility condition between a generalized metric and a small (non-maximal rank) Dirac structure in an exact Courant algebroid found in the context of the gauging of strings and formulated by means of two connections in purely Dirac-geometric terms. The resulting notion, a transverse generalized m…

We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra $\mathfrak{g}$ leads naturally to the appearance of the "generalized tangent bundle" $\mathbb{T}M \equiv TM \oplus T^*M$ by means of composite fields. Gauge transformations of the composite fields foll…

The paper explores gauge theory invariants and their duals via topological-holomorphic twist.

Study of symmetries in 2D Yang-Mills theory, including orbifolds and higher forms.

Study connections on Lie and Courant algebroids, defining basic curvature and Atiyah cocycle.

We review the construction of homological evolutionary vector fields on infinite jet spaces and partial differential equations. We describe the applications of this concept in three tightly inter-related domains: the variational Poisson formalism (e.g., for equations of Korteweg-de Vries type), geometry of Liouville-ty…

This is the second in a series of papers discussing in the framework of gerbe theory canonical and geometric aspects of the 2d nonlinear sigma model in the presence of conformal defects in the worldsheet. Employing the formal tools worked out in the first paper of the series, 1101.1126 [hep-th], a thorough analysis of …

Novel gauge-theoretic Floer homologies defined from 5d N=2 theory, linking 4, 3, and 2-manifolds.

In this paper, we provide a construction of a state-sum model for finite gauge-group Dijkgraaf-Witten theory on surfaces with codimension 1 defects. The construction requires not only that the triangulation be subordinate to the filtration, but flag-like: each simplex of the triangulation is either disjoint from the de…

Lectures detail field theory dynamics and exact WKB analysis.

Novel gauge-theoretic Floer homologies defined for 7, 6, and 5-manifolds.

We consider the Dirac equation in flat Minkowski 3-space and rewrite it as the Maxwell equation in Minkowski 4-space with torsion. The torsion tensor is defined as the dual of the electromagnetic vector potential. Our model clearly distinguishes the electron and the positron without resorting to "negative frequencies":…

The algebra of differential geometry operations on symmetric tensors over constant curvature manifolds forms a novel deformation of the sl(2,R) [semidirect product] R^2 Lie algebra. We present a simple calculus for calculations in its universal enveloping algebra. As an application, we derive generating functions for t…

We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riema…

Generalizing our ideas in [arXiv:1006.3313], we explain how topologically-twisted N=2 gauge theory on a four-manifold with boundary, will allow us to furnish purely physical proofs of (i) the Atiyah-Floer conjecture, (ii) Munoz's theorem relating quantum and instanton Floer cohomology, (iii) their monopole counterparts…

Proposes a model to generate 3D-aware images from 2D images.

Improved lattice field theory simulations with local-Autoregressive Conditional Normalizing Flow.

Paper introduces Tensor Gauge Flow Models for better data encoding.

We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface $Σ$ that separates two subsystems of quantum strongly coupled ${\mathcal{N}}=4$ SU(N) superconformal gauge theory. We extend this result and calculate en…

The paper establishes T-duality for 2D σ-models with H-flux.

2D CNNs approximate Korobov functions with near-optimal rates.

DISPR uses diffusion models to predict 3D cell shapes from 2D images.

Gauge Flow Models use a learnable Gauge Field in Generative Flow Models.

There is a growing need for fast and accurate methods for testing developmental neurotoxicity across several chemical exposure sources. Current approaches, such as in vivo animal studies, and assays of animal and human primary cell cultures, suffer from challenges related to time, cost, and applicability to human physi…

New K-theory approach classifies anyonic topological phases in 2D semimetals.

iSTFTNet2 improves iSTFTNet's speed and lightness with 1D-2D CNN.

Paper extends 2D ZSAD to 3D MRI without training, achieving robust anomaly detection.

L-CNNs preserve gauge symmetry in lattice simulations.

Transformer-M learns molecular data in 2D or 3D formats.

Higher Gauge Flow Models integrate higher geometry and symmetries into Generative Flow Models.

New method reconstructs 3D shapes from 2D images using Kendall's shape space.

New model preserves symmetry in multivariate time series, improving performance.

Study glues 2D hyperbolic manifolds, deriving mass formulas.

Optimizes master faces for 2D and 3D face verification using evolutionary algorithms and neural networks.

The G/G WZW model results from the WZW-model by a standard procedure of gauging. G/G WZW models are members of Dirac sigma models, which also contain twisted Poisson sigma models as other examples. We show how the general class of Dirac sigma models can be obtained from a gauging procedure adapted to Lie algebroids in …

New neural model processes 2D data with long-range dependencies efficiently.

Modeling financial market dynamics with 2D Levy flights.

New method for optimizing risk in financial models using Fourier transforms.