Related papers: An invitation to algebraic topological string theo…
This note is supposed to be an introduction to those concepts of toric geometry that are necessary to understand applications in the context of string and F-theory dualities. The presentation is based on the definition of a toric variety in…
The note complements topological aspects of the theory of chiral algebras.
These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A…
The purpose of the present paper is the communication of some results and observations which shed new light on the algebraic structure of the algebra of string observables both in the classical and in the quantum theory.
This paper is an exposition of the new subject of String Topology. We present an introduction to this exciting new area, as well as a survey of some of the latest developments, and our views about future directions of research. We begin…
Deformations of topological open string theories are described, with an emphasis on their algebraic structure. They are encoded in the mixed bulk-boundary correlators. They constitute the Hochschild complex of the open string algebra -- the…
The possible tensor constructions of open string theories are analyzed from first principles. To this end the algebraic framework of open string field theory is clarified, including the role of the homotopy associative A_\infty algebra, the…
The closed topological vertex is the simplest ``off-strip'' case of non-compact toric Calabi-Yau threefolds with acyclic web diagrams. By the diagrammatic method of topological vertex, open string amplitudes of topological string theory…
In this paper the $c=1$ string theory is studied from the point of view of topological field theories. Calculations are done for arbitrary genus. A change in the prescription is proposed, which reproduces the results of the $1/x^2$ deformed…
This is a survey article on the recent development of "stringy geometry and topology of orbifolds", a new subject of mathematics motivated by orbifold string theory.
This paper aims to provide a careful and self-contained introduction to the theory of topological degree in Euclidean spaces. It is intended for people mostly interested in analysis and, in general, a heavy background in algebraic or…
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…
The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global…
We describe a topological string theory which reproduces many aspects of the 1/N expansion of SU(N) Yang-Mills theory in two spacetime dimensions in the zero coupling (A=0) limit. The string theory is a modified version of topological…
In these lectures, we review the main properties of the topological theory obtained by twisting the N=2 two-dimensional superconformal algebra, associated to supersymmetric string compactifications. In particular, we describe a set of…
I present a new class of topological string theories, and discuss them in two dimensions as candidates for the string description of large-$N$ QCD. The starting point is a new class of topological sigma models, whose path integral is…
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
We construct a universal envelope for any Poisson- and Gerstenhaber algebra. While the deformation theory of Poisson algebras seems to be partially trivial, results from string- and M-theory suggest a rich deformation theory of Gerstenhaber…
This is a brief overview on the current status of string theory for non-specialists. The purpose is to give an aspect on the nature of string theory as a unified theory of all interactions including quantum gravity and to discuss future…
In arXiv:0905.3629 we described a new class of N=2 topological amplitudes that depends both on vector and hypermultiplet moduli. Here we find that this class is actually a particular case of much more general topological amplitudes which…