Conformal Field Theory and algebraic structure of gauge theory

Q-structure of Conformal Field Theory with Gauge Symmetries

Introduction It is well-known that abelian conformal eld theory has rich arithmetic structure (see, for example [DKK], [KSU1], [KSU2], [KUS3]). It is natural to ask whether this is also the case for no-abelian conformal eld theory. For the rst step to study arithmetic properties of non-abelian conformal eld theory, in the present notes we shall study the eld of de nition of conformal eld theory...

Auxiliary field in conformal gauge theory.

Operads and Conformal Field Theory Lecture 1: Conformal Field Theory

Physicists have developed very advanced methods to compute such integrals. For example, the famous Feynman diagram technique allows us to compute the above integral for a rather particular function S(x), a small perturbation of a positive de nite quadratic form in R . Sometimes, elaborate techniques of physicists to compute simple things nd an amazing application to very general things in mathe...

Modular data: the algebraic combinatorics of conformal field theory

This paper is primarily intended as an introduction for mathematicians to some of the rich algebraic combinatorics arising in for instance conformal field theory (CFT). It is essentially self-contained, apart from some of the background motivation (Section I) and examples (Section III) which are included to give the reader a sense of the context. Detailed proofs will appear elsewhere. The theor...

Gauge Symmetry in Background Charge Conformal Field Theory *

We present a mechanism to construct four-dimensional charged massless Ramond states using the discrete states of a fivebrane Liouville internal conformal field theory. This conformal field theory has background charge, and admits an inner product which allows positive norm states. A connection among supergravity soliton solutions, Liouville conformal field theory, non-critical string theory and...