arXiv research

Constructs combinatorial 2D topological field theories from cyclic A-infinity algebras.

Open 2D TFTs extend to closed theories with circle value as Hochschild homology.

The paper extends topological field theory to noncompact surfaces using symmetric powers.

Paper connects 3D gravity averages to 2D CFT correlators.

The paper develops a theory linking Hamiltonian and quasi-Hamiltonian manifolds.

Constructs new topological theories in 2D not fitting standard axioms.

Constructs algorithms to recognize and classify 2D surfaces.

New geometric perspective for optimal learning on hexagonal structures.

We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1,0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0,1) supersymmetry and, possibly, a residual flavor symmetry. …

Estimates quantum cohomology complexity for Fano varieties and homogeneous spaces.

3D dual field theories for Virasoro minimal models constructed using Seifert fiber spaces.

Cone structures in quantum field theory linked to information geometry.

Generic singularities of line fields have been studied for lines of principal curvature of embedded surfaces. In this paper we propose an approach to classify generic singularities of general line fields on 2D manifolds. The idea is to identify line fields as bisectors of pairs of vector fields on the manifold, with re…

Survey on matrix hydrodynamics, a 2D fluid model.

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

We derive the general state sum construction for 2D topological quantum field theories (TQFTs) with source defects on oriented curves, extending the state-sum construction from special symmetric Frobenius algebra for 2-D TQFTs without defects (cf. Lauda \& Pfeiffer \cite{LP}). From the extended Pachner moves (Crane \& …

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

The study classifies Kähler-Frobenius manifolds and their properties.

To formulate the universal constraints of quantum statistics data of generic long-range entangled quantum systems, we introduce the geometric-topology surgery theory on spacetime manifolds where quantum systems reside, cutting and gluing the associated quantum amplitudes, specifically in 2+1 and 3+1 spacetime dimension…

Lectures detail field theory dynamics and exact WKB analysis.

We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of potential flat torsionless submanifolds. We show that all potential flat…

Summing over 3-manifolds using TQFT partition functions.

Lectures on topological field theories and differential cohomology.

Using probabilistic methods, we first define Liouville quantum field theory on Riemann surfaces of genus $\mathbf{g}\geq 2$ and show that it is a conformal field theory. We use the partition function of Liouville quantum field theory to give a mathematical sense to Polyakov's partition function of noncritical bosonic s…

The data of a "2D field theory with a closed string compactification" is an equivariant chain level action of a cell decomposition of the union of all moduli spaces of punctured Riemann surfaces with each component compactified as a pseudomanifold with boundary. The axioms on the data are contained in the following ass…

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 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 proves UV finiteness and vanishing anomalies for hybrid topological-holomorphic field theories.

Study Ricci vector fields on 2D space with diagonal metrics.

In this paper we address several aspects of flat Bogomolnyi-Prasad-Sommerfeld (BPS) domain walls together with their Lorentz invariant vacua of 4d N=1 supergravity coupled to a chiral multiplet. The scalar field spans a one-parameter family of 2d Kähler manifolds satisfying a Kähler-Ricci flow equation. We find that BP…

The paper quantizes hybrid topological-holomorphic field theories on $\mathbb{R}^m imes \mathbb{C}^n$.

Curvature of 2D subsets preserved in their space.

Classifies 2D TQFTs for orientable cobordisms using additional data.

Topology guidance controls generative model outputs by specifying topological features.

Observable structures of a topological field theory of AKSZ type are analyzed. From a double (or multiple) complex structure of observable algebras, new topological invariants are constructed. Especially, Donaldson polynomial invariants and their generalizations are constructed from a topological field theory of AKSZ t…

We extend the topological field theory (``itsy bitsy topological field theory"') of our previous work from mod-2 to twisted coefficients. This topological field theory is derived from sutured Floer homology but described purely in terms of surfaces with signed points on their boundary (occupied surfaces) and curves on …

Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.

There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field theory combined.

It is well-known that classical two-dimensional topological field theories are in one-to-one correspondence with commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by open-closed two-dimensional topological field theories. In this paper we extend o…

The abstract discusses connecting quantum mechanics and algebraic index theories.

In this paper we give a characterization of 2-dimensional topological field theories over a space $X$ as Frobenius bundles with connections over $LX$, the free loop space of $X$. This is a generalization of the folk theorem stating that 2-dimensional topological field theories (over a point) are described by finite-dim…

This paper proposes an axiomatic for Cyclic Foam Topological Field theories. That is Topological Field theories, corresponding to String theories, where particles are arbitrary graphs. World surfaces in this case are two-manifolds with one-dimensional singularities. We proved that Cyclic Foam Topological Field theories…

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

We expand Topological Field Theory on some special CW-complexes (brane complexes). This Brane Topological Field Theory one-to-one corresponds to infinite dimensional Frobenius Algebras, graduated by CW-complexes of lesser dimension. We define general and regular Hurwitz numbers of brane complexes and prove that they ge…

Introduces Lax-Kirchhoff moduli spaces for quivers and Lie groups.

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

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

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…