Related papers: Integrable Lattice Models and Holography

This paper studies novel four-dimensional integrable field theories that are deformations of self-dual Yang-Mills. They are engineered by considering holomorphic Chern-Simons and BF type theories on covers of twistor space obtained by…

For $n \geq 2$, consider $\mathbb{Z}^n$ as a lattice graph. We explore a generalized Chern-Simons equation on $\mathbb{Z}^n$. Employing the method of exhaustion, we prove that there exists a global solution that also qualifies as a…

The Hilbert space of level $q$ Chern-Simons theory of gauge group $G$ of the ADE type quantized on $T^2$ can be represented by points that lie on the weight lattice of the Lie algebra $\mathfrak{g}$ up to some discrete identifications. Of…

Levin and Wen [Phys. Rev. B 71, 045110 (2005)] have recently given a lattice Hamiltonian description of doubled Chern-Simons theories. We relate the partition function of these theories to an expectation of Wilson loops that form a link in…

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…

There are two natural Chern-Simons theories associated with the embedding of a three-dimensional surface in Euclidean space; one is constructed using the induced metric connection -- it involves only the intrinsic geometry, the other is…

The dynamics of Wilson loops are governed by an infinite set of Schwinger-Dyson equations and trace relations. In the context of the lattice positivity bootstrap, a central challenge is determining a dynamically independent basis of these…

Based on recent results obtained by the authors on the inverse scattering method of the vector nonlinear Schr\"odinger equation with integrable boundary conditions, we discuss the factorization of the interactions of N-soliton solutions on…

We discuss methods for calculating Chern numbers of two-dimensional lattice systems using spiral boundary conditions, which sweep all lattice sites in one-dimensional order. Specifically, we establish the one-dimensional representation of…

We use 3d bosonization dualities to derive new non-supersymmetric dualities between bosonic quiver theories in $2+1$ dimensions. It is shown that such dualities are a natural non-Abelian generalization of the bosonic particle-vortex…

It is known that integrable models associated to rational $R$ matrices give rise to certain non-abelian symmetries known as Yangians. Analogously `boundary' symmetries arise when general but still integrable boundary conditions are…

We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d $\mathcal{N} = 1$…

I consider the classical Kac-Moody algebra and Virasoro algebra in Chern-Simons theory with boundary within the Dirac's canonical method and Noether procedure. It is shown that the usual (bulk) Gauss law constraint becomes a second-class…

We argue that a certain twisted supersymmetric Yang-Mills theory in three dimensions with gauge group SU(2) possesses a set of topological observables whose expectation values can be computed in a related Chern Simons theory. This Chern…

We construct the actions of a very broad family of 2d integrable $\sigma$-models. Our starting point is a universal 2d action obtained in [arXiv:2008.01829] using the framework of Costello and Yamazaki based on 4d Chern-Simons theory. This…

Toroidally compactified Yang-Mills theory on the lattice is studied by using the Hybrid Monte Carlo algorithm. When the compact dimensions are small, the theory naturally reduces to Yang-Mills with scalars. We confirm previous analytical…

A generalization of the Yang-Baxter equation is proposed. It enables to construct integrable two-dimensional lattice models with commuting two-layer transfer matrices, while single-layer ones are not necessarily commutative. Explicit…

We study four-dimensional $\mathrm{SU}(N)$ Yang-Mills theory on $\mathbb{R} \times \mathbb{T}^3=\mathbb{R} \times S^1_A \times S^1_B \times S^1_C$, with a twisted boundary condition by a $\mathbb{Z}_N$ center symmetry imposed on $S^1_B…

Two series of integrable theories are constructed which have soliton solutions and can be thought of as generalizations of the sine-Gordon theory. They exhibit internal symmetries and can be described as gauged WZW theories with a potential…

In this paper, we apply the proper-time method to generate the Lorentz-violating Chern-Simons terms in the four-dimensional Yang-Mills and non-linearized gravity theories. It is shown that the coefficient of the induced Chern-Simons term is…