Related papers: The Fourier-Mukai Transform in String Theory
This article contains a short review of the current status of string theory.
In the past three years our views on how the standard model of particle physics could be embedded into string theory have dramatically changed. The heterotic string is no longer the only possibility for such an embedding and other…
We study the interplay between the Fourier-Mukai transform and the decomposition theorem for an integrable system $\pi: M \rightarrow B$. Our main conjecture is that the Fourier-Mukai transform of sheaves of K\"ahler differentials, after…
I review recent progress on the connection between string theory and quantum chromodynamics in the context of the gauge/gravity duality. Emphasis is placed on conciseness and conceptual aspects rather than on technical details. Topics…
We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. Main results provide fractional…
String theory is accused by some of its critics to be a purely abstract mathematical discipline, having lost the contact to the simple yet deeply rooted questions which physics provided until the beginning of this century. We argue that, in…
This is an informal introduction to the concept of reflexive polyhedra and some of their most important applications in perturbative and non-perturbative string physics. Following the historical development, topics like mirror symmetry,…
This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…
The spectral analysis of the operator Fourier truncated on the positive half-axis is done.
This is the written version of a set of introductory lectures on string theory.
Starting with exact solutions to string theory on curved spacetimes we obtain deformations that represent gravitational shock waves. These may exist in the presence or absence of sources. Sources are effectively induced by a tachyon field…
This paper is a rudimentary introduction, geared at non-specialists, to how noncommutative field theories arise in physics and their applications to string theory, particle physics and condensed matter systems.
Talk given at ICM '98, Berlin, reviewing some of the recent developments in understanding of string theory for a mathematical audience (to appear in Documenta Mathematica).
I briefly review several important formal theory developments in quantum field theory and string theory that were reported at ICHEP conferences in past decades, and explain how they underlie a new research area referred to as physical or…
Fourier and fractional-Fourier transformations are widely used in theoretical physics. In this paper we make quantum perspectives and generalization for the fractional Fourier transformation (FrFT). By virtue of quantum mechanical…
Progress on the physics of strings in curved spacetime are comprehensively reviewed.We start by showing through renormalization group arguments that a meaningful quantum theory of gravity must be finite and must include all particle…
This is a brief reminder, with extensions, from a different angle and for a less specialized audience, of my presentation at WGMP32 in July 2013, to which I refer for more details on the topics hinted at in the title, mainly deformation…
The 1988 book, now free, with corrections and bookmarks (for pdf).
In this article, prepared for the book "The birth of string theory", I recall the sequence of ideas which led to non-critical strings and gauge/strings duality. I also comment on some promising future directions.
String diagrams are a powerful and intuitive graphical syntax, originated in the study of symmetric monoidal categories. In the last few years, they have found application in the modelling of various computational structures, in fields as…