Related papers: The Fourier-Mukai Transform in String Theory
I review recent progress in understanding non-perturbative aspects of string theory, quantum gravity and non-commutative geometry using lattice methods.
There is a beautiful correspondence between configurations of lines on a rational surface and tautological bundles over that surface. We extend this correspondence to families, by means of a generalized Fourier-Mukai transform that relates…
There have been many remarkable developments in our understanding of superstring theory in the past few years, a period that has been described as ``the second superstring revolution.'' Several of them are discussed here. The presentation…
This article provides some historical background and then reviews developments in string theory over the last twenty-five years or so. Both perturbative and non-perturbative approaches to string theory are surveyed and their impact on how…
The status of string theory is reviewed, and major recent developments - especially those in going beyond perturbation theory in the string theory and quantum field theory frameworks - are discussed. This analysis helps better understand…
I review some of the recent progress in two-dimensional string theory, which is formulated as a sum over surfaces embedded in one dimension.
This review article was first published in 2008 as chapter 11 in the book "Fast Fourier Transforms," edited by C. S. Burrus, for the Connexions project at Rice University, which is sadly no longer online. It gives a high-level overview of…
These notes are based on lectures given by Michael Green during Part III of the Mathematics Tripos (the Certificate for Advanced Study in Mathematics) in the Spring of 2003. The course provided an introduction to string theory, focussing on…
We consider relationships between families of K3 surfaces, in the context of string theory. An important ingredient of string theory also of interest in algebraic geometry is T-duality. Donagi and Pantev have extended the original duality…
We study relative Fourier-Mukai transforms on genus one fibrations with section, allowing explicitly the total space of the fibration to be singular and non-projective. Grothendieck duality is used to prove a skew-commutativity relation…
Given a Fourier-Mukai functor $\Phi$ in the general setting of singular schemes, under various hypotheses we provide both left and a right adjoints to $\Phi$, and also give explicit formulas for them. These formulas are simple and natural,…
In 1996, Rothstein and Laumon simultaneously constructed a Fourier-Mukai transform for D-modules over a locally noetherian base of characteristic 0. This functor induces an equivalence of categories between quasi-coherent sheaves of…
The aim of these notes is to give recent developments in string theory. In particular, we discuss the string spectrums, compactifications, brane physics and dualities.
We present a brief review of selected topics in noncommutative field theories ranging from its revival in string theory, its influence on quantum field theories, its possible experimental signatures and ending with some applications in…
We give an introduction to the statistical approach to studying vacua of string/M theory, and discuss recent results of Ashok and Douglas on counting supersymmetric flux vacua in type IIb Calabi-Yau compactification. To appear in the…
In this article we examine the compatibility of some recent results, results relating M-Theory to String Theory, with the string-string duality conjecture in six-dimensions. In particular, we rederive the relation between M-Theory and Type…
This book provides an introduction to string field theory (SFT). String theory is usually formulated in the worldsheet formalism, which describes a single string (first-quantization). While this approach is intuitive and could be pushed far…
String theory is the most promising candidate theory for a unified description of all fundamental forces exist in the nature. It provides a mathematical framework that combine quantum theory with Einstein's general theory of relativity. But…
This essay presents a critical evaluation of the concepts of string theory and its impact on particle physics. The point of departure is a historical review of four decades of ST within the broader context of six decades of failed attempts…
This is a summary of a talk at Strings2000 explaining three ways in which string theory and M-theory are related to the mathematics of K-theory.