Related papers: Notes on Seiberg-Witten Gauge Theory
The properties of the N=2 SUSY gauge theories underlying the Seiberg-Witten hypothesis are discussed. The main ingredients of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating…
These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.
We describe how the ingredients and results of the Seiberg-Witten solution to N=2 supersymmetric U(N) gauge theory may be obtained from a matrix model.
Invited talk at the PSI Summer School on Physics with Neutrinos, Zuoz, Switzerland, August 4-10, 1996.
These are extended notes of a lecture about the papers 1207.1883 by Esnault-Levine-Wittenberg and 1308.3024 by Wittenberg. The aim is to define the Esnault-Levine-Wittenberg indices, establish their basic properties amd to pose several…
This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…
Introductory lectures notes on cosmology, aimed at master students in physics and based on a course held at Milano University (in Italian).
These notes represent a much expanded and updated version of the \textquotedblleft mini course\textquotedblright that the author gave at the ETH (Z\"{u}rich) and the University of Z\"{u}rich in February of 1995. The purpose of these notes…
The formulation of Seiberg-Witten maps from the point of view of consistent deformations of gauge theories in the context of the Batalin-Vilkovisky antifield formalism is reviewed. Some additional remarks on noncommutative Yang-Mills theory…
These notes are for the author's lectures, "Integral Reduction and Applied Algebraic Geometry Techniques" in the School and Workshop on Amplitudes in Beijing 2016. I introduce the applications of algebraic geometry methods on multi-loop…
In this paper, we describe a method for obtaining the nonabelian Seiberg-Witten map for any gauge group and to any order in theta. The equations defining the Seiberg-Witten map are expressed using a coboundary operator, so that they can be…
The Seiberg-Witten map links noncommutative gauge theories to ordinary gauge theories, and allows to express the noncommutative variables in terms of the commutative ones. Its explicit form can be found order by order in the noncommutative…
We derive an exact expression for the Seiberg-Witten map of noncommutative gauge theory. It is found by studying the coupling of the gauge field to the Ramond-Ramond potentials in string theory. Our result also proves the earlier conjecture…
Four-dimensional N=2 gauge theories may be obtained from configurations of D-branes in type IIA string theory. Unitary gauge theories with two-index representations, and orthogonal and symplectic gauge theories, are constructed from…
The scope of this review is to give a pedagogical introduction to some new calculations and methods developed by the author in the context of quantum groups and their applications. The review is self- contained and serves as a "first aid…
These are lecture notes for a one semester introductory course I gave at Indiana University. The goal was to make this exposition as clear and elementary as possible. A particular emphasis is given on examples involving SU(1,1). These notes…
These are the lecture notes (in Italian) of a course held in Perugia, Italy, during the summer 2002. They concern the basic facts on the iterative solution of linear systems. The course is self-contained and requires only basic knowledge of…
These notes are dedicated to whom may be interested in algorithms, Markov chain, coupling, and graph theory etc. I present some preliminaries on coupling and explanations of the important formulas or phrases, which may be helpful for us to…
This is an expository article on the techniques of quantization as they are applied to Gromov-Witten theory and related areas.
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.