Seiberg-Witten prepotential from instanton counting
Abstract : Direct evaluation of the Seiberg-Witten prepotential is accomplished following the localization programme suggested some time ago. Our results agree with all low-instanton calculations available in the literature. We present a two-parameter generalization of the Seiberg-Witten prepotential, which is rather natural from the M-theory/five dimensional perspective, and conjecture its relation to the tau-functions of KP/Toda hierarchy. To Arkady Vainshtein on his 60th anniversary
Target space symmetries in topological theories I.
Abstract : We study realization of the target space diffeomorphisms in the type C topological string. We found that the charges, which generate transformations of the boundary observables, form an algebra, which differs from that of bulk charges by the contribution of the bubbled disks. We discuss applications to noncommutative field theories.
Abstract : We find a new gauge in which U(1) noncommutative instantons are explicitly non-singular on noncommutative R^4. We also present a pedagogical introduction to the noncommutative gauge theories.
Trieste lectures on solitons in noncommutative Gauge theories
Abstract : We present a pedagogical introduction into noncommutative gauge theories, their stringy origin, and non-perturbative effects, including monopole and instanton solutions.
Lectures on open strings, and noncommutative Gauge theories
Abstract :The background independent formulation of the gauge theories on D-branes in flat space-time is considered, some examples of the solutions of their equations of motion are presented, the solutions of Dirac equation in these backgrounds are analyzed, and the generalizations to the curved spaces, like orbifolds, conifolds, and K3 surfaces are discussed.
Milne Universe, Tachyons, and quantum group
Abstract : We analyze the spectrum of the bosonic and superstring on the orbifold of the space-time by a boost, leading to the cosmological singularity. We show that the modular invariance leads to the spectrum where the twisted sector tachyon, together with all other twisted sector fields, present in the Euclidean version of the orbifold, is absent. This makes impossible to resolve the singularity by a marginal deformation of the worldsheet CFT. We also establish a relation between the resolution of rotational orbifolds in Euclidean and Lorentzian setups, and quantum groups. The analysis confirms the impossibility of resolving the cosmological orbifold singularity.
Abstract : We review the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory, and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, both on the classical and quantum level. To appear in Reviews of Modern Physics.