Related papers: Lectures on Two-Dimensional Noncommutative Gauge T…
In this lecture we give an elementary introduction to the natural realization of non-perturbative N=2 quantum field theories as a low energy limit of classical string theory. We review a systematic construction of six, five, and four…
A modification of the gauge theory is proposed, in which the set of generalized coordinates is supplemented with symmetry transformation parameters, and a condition is additionally imposed on the latter that ensures the classical character…
We describe and solve a double scaling limit of large N Yang-Mills theory on a two-dimensional torus. We find the exact strong-coupling expansion in this limit and describe its relation to the conventional Gross-Taylor series. The limit…
We consider a model of classical noncommutative particle in an external electromagnetic field. For this model, we prove the existence of generalized gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is discussed,…
We formulate and explore the physical implications of a new translation gauge theory of gravity in flat space-time with a new Yang-Mills action, which involves quadratic gauge curvature and fermions. The theory shows that the presence of an…
T-duality of gauge theories on a noncommutative $T^d$ can be extended to include fields with twisted boundary conditions. The resulting T-dual theories contain novel nonlocal fields. These fields represent dipoles of constant magnitude.…
It is proposed an integral formulation of classical Yang-Mills equations in the presence of sources, based on concepts in loop spaces and on a generalization of the non-abelian Stokes theorem for two-form connections. The formulation leads…
We argue that, ideally, the ways to measure magnitudes in non-quantum theories of physics (spacetime, field theory), limit drastically their possible mathematical models. In particular, gauge invariance in the Yang-Mills framework, is a…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
I review my results about noncommutative gauge theories and about the relation of these theories to M(atrix) theory following my lecture on ICMP 2000.
I revisit a basic question about the noncommutative Yang-Mills theory: if it exists or not, or more precisely, whether a nonperturbative formulation exists. As the most promising approach, I consider a formulation based on matrix models. It…
This is an overview of recent results aimed at developing a geometry of noncommutative tori with real multiplication, with the purpose of providing a parallel, for real quadratic fields, of the classical theory of elliptic curves with…
We present a powerful method to generate various equations which possess the Lax representations on noncommutative (1+1) and (1+2)-dimensional spaces. The generated equations contain noncommutative integrable equations obtained by using the…
Contribution to the Proceedings of the International Congress of Mathematicians 1994. We review recent developments in the physics and mathematics of Yang-Mills theory in two dimensional spacetimes. This is a condensed version of a…
The correlation functions of open Wilson line operators in two-dimensional Yang-Mills theory on the noncommutative torus are computed exactly. The correlators are expressed in two equivalent forms. An instanton expansion involves only…
N=2 supersymmetric Yang--Mills theories coupled to matter are considered in the Wess--Zumino gauge. The supersymmetries are realized nonlinearly and the anticommutator between two susy charges gives, in addition to translations, gauge…
I review results from recent investigations of anomalies in fermion--Yang Mills systems in which basic notions from noncommutative geometry (NCG) where found to naturally appear. The general theme is that derivations of anomalies from…
This is the text of a series of five lectures given by the author at the "Second Annual Spring Institute on Noncommutative Geometry and Operator Algebras" held at Vanderbilt University in May 2004. It is meant as an overview of recent…
The paper addresses the question whether in four spacetime dimensions, besides standard supergravity theories, field theories exist whose symmetries include local spacetime translations and supersymmetries generated by transformations whose…
A generalization of the two-dimensional Yang-Mills and generalized Yang-Mills theory is introduced in which the building B-F theory is nonlocal in the auxiliary field. The classical and quantum properties of this nonlocal generalization are…