相关论文: Yang-Baxter random fields and stochastic vertex mo…

The Faddeev-Volkov solution of the star-triangle relation is connected with the modular double of the quantum group U_q(sl_2). It defines an Ising-type lattice model with positive Boltzmann weights where the spin variables take continuous…

Functional equations methods are a fundamental part of the theory of Exactly Solvable Models in Statistical Mechanics and they are intimately connected with Baxter's concept of commuting transfer matrices. This concept has culminated in the…

We introduce the notion of finite BRST-antiBRST transformations, both global and field-dependent, with a doublet $\lambda_{a}$, $a=1,2$, of anticommuting Grassmann parameters and find explicit Jacobians corresponding to these changes of…

We propose a nonperturbative approach to nonabelian two-form gauge theory. We formulate the theory on a lattice in terms of plaquette as fundamental dynamical variable, and assign U(N) Chan-Paton colors at each boundary link. We show that,…

Using topological Yang-Mills theory as example, we discuss the definition and determination of observables in topological field theories (of Witten-type) within the superspace formulation proposed by Horne. This approach to the equivariant…

We consider a matrix branching random walk on the semi-group of nonnegative matrices, where we are able to derive, under general assumptions, an analogue of Biggins' martingale convergence theorem for the additive martingale $W_n$, a spinal…

We perform the stochastic quantization of Yang-Mills theory in configuration space and derive the Faddeev-Popov path integral density. Based on a generalization of the stochastic gauge fixing scheme and its geometrical interpretation this…

A four-dimensional ${\rm SU}(4)$ confining Yang-Mills field, coupled to a fundamental fermion field and a bi-fundamental scalar field, has excitations with spin-2, but no other quantum numbers. These spin-2 excitations can be light or can…

In this article, a system of Yang-Baxter-type matrix equations is studied, $XAX=BXB$, $XBX=AXA$, which "generalizes" the matrix Yang-Baxter equation and exhibits a broken symmetry. We investigate the solutions of this system from various…

We construct off-shell vertex operators for the bosonic spinning particle. Using the language of homotopy algebras, we show that the full nonlinear structure of Yang-Mills theory, including its gauge transformations, is encoded in the…

We continue our systematic construction of Baxter Q-operators for spin chains, which is based on certain degenerate solutions of the Yang-Baxter equation. Here we generalize our approach from the fundamental representation of gl(n) to…

The Yang-Baxter (YB) deformations of Wess-Zumino-Witten (WZW) model on the Heisenberg Lie group ($H_4$) are examined. We proceed to obtain the nonequivalent solutions of (modified) classical Yang-Baxter equation ((m)CYBE) for the $ h_4$ Lie…

The conventional Rosenfeld-Bergmann-Dirac constrained Hamiltonian algorithm applied to Einstein-Yang-Mills theory is shown to be equivalent to a local gauge theoretic extension of Cartan's invariant integral approach to classical mechanics.…

The entire geometric formulations of the BRST and the anti-BRST structures are worked out in presence of the Nakanishi-Lautrup field. It is shown that in the general form of gauge fixing mechanisms within the Faddeev-Popov quantization…

We construct a nonperturbative regularization for Euclidean noncommutative supersymmetric Yang-Mills theories with four (N= (2,2)), eight (N= (4,4)) and sixteen (N= (8,8)) supercharges in two dimensions. The construction relies on orbifolds…

Boltzmann-Gibbs random fields are defined in terms of the exponential expression exp(-H), where H is a suitably defined energy functional of the field states x(s). This paper presents a new Boltzmann-Gibbs model which features local…

This talk is inspired by two previous ICM talks, by V.Drinfeld (1986) and G.Felder (1994). Namely, one of the main ideas of Drinfeld's talk is that the quantum Yang-Baxter equation (QYBE), which is an important equation arising in quantum…

We study the stochastic six vertex model and prove that under weak asymmetry scaling (i.e., when the parameter $\Delta\to 1^+$ so as to zoom into the ferroelectric/disordered phase critical point) its height function fluctuations converge…

The existence of interacting higher-spin theories is tightly constrained by many no-go theorems. In this paper, we construct a chiral, higher-spin generalization of Yang-Mills theory in flat space which avoids these no-go theorems and has…

In this paper we develop a quantitative Harris theorem with effective control over the constants. A benefit of our methodology is the decoupling of the small set and Lyapunov-Foster Drift conditions. Our methodology allows any small set and…