Related papers: Instanton Expansion of Noncommutative Gauge Theory…
These notes comprise the first of two articles devoted to the construction of exact solutions of noncommutative gauge theory in two spacetime dimensions. This first part deals solely with the classical theory on a noncommutative torus.…
These notes comprise the second part of two articles devoted to the construction of exact solutions of noncommutative gauge theory in two spacetime dimensions. Here we shall deal with the quantum field theory. Topics covered include an…
We use the exact instanton expansion to illustrate various string characteristics of noncommutative gauge theory in two dimensions. We analyse the spectrum of the model and present some evidence in favour of Hagedorn and fractal behaviours.…
We describe the statistical mechanics of a melting crystal in three dimensions and its relation to a diverse range of models arising in combinatorics, algebraic geometry, integrable systems, low-dimensional gauge theories, topological…
We survey some of the AGT relations between N=2 gauge theories in four dimensions and geometric representations of symmetry algebras of two-dimensional conformal field theory on the equivariant cohomology of their instanton moduli spaces.…
The instanton contributions to the partition function and to homologically trivial Wilson loops for a U(N) Yang-Mills theory on a torus $T^2$ are analyzed. An exact expression for the partition function is obtained as a sum of contributions…
The twisted Eguchi-Kawai (TEK) model provides a non-perturbative definition of noncommutative Yang-Mills theory: the continuum limit is approached at large $N$ by performing suitable double scaling limits, in which non-planar contributions…
We present a novel formulation of the instanton equations in 8-dimensional Yang-Mills theory. This formulation reveals these equations as the last member of a series of gauge-theoretical equations associated with the real division algebras,…
The results obtained by Seiberg and Witten for the low-energy Wilsonian effective actions of N=2 supersymmetric theories with gauge group SU(2) are in agreement with instanton computations carried out for winding numbers one and two. This…
We review some recent progress in understanding the relation between a six dimensional topological Yang-Mills theory and the enumerative geometry of Calabi-Yau threefolds. The gauge theory localizes on generalized instanton solutions and is…
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…
Cohomological Yang-Mills theory is formulated on a noncommutative differentiable four manifold through the $\theta$-deformation of its corresponding BRST algebra. The resulting noncommutative field theory is a natural setting to define the…
After a brief review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, we present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus in two…
This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral…
Interpreting the coordinates of the quantum Euclidean space R_q^4 [the SO_q(4)-covariant noncommutative space] as the entries of a ``q-quaternion matrix'' we construct (anti)instanton solutions of a would-be q-deformed su(2) Yang-Mills…
We construct (anti)instanton solutions of a would-be q-deformed su(2) Yang-Mills theory on the quantum Euclidean space R_q^4 [the SO_q(4)-covariant noncommutative space] by reinterpreting the function algebra on the latter as a q-quaternion…
We describe how and to what extent the noncommutative two-torus can be approximated by a tower of finite-dimensional matrix geometries. The approximation is carried out for both irrational and rational deformation parameters by embedding…
This review paper is a continuation of hep-th/0012145 and it deals primarily with noncommutative ${\mathbb R}^{d}$ spaces. We start with a discussion of various algebras of smooth functions on noncommutative ${\mathbb R}^{d}$ that have…
We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its…
We give a mathematically rigorous proof of Nekrasov's conjecture: the integration in the equivariant cohomology over the moduli spaces of instantons on $\mathbb R^4$ gives a deformation of the Seiberg-Witten prepotential for N=2 SUSY…