On the Large N Limit of Conformal Field Theory

TL;DR

This paper develops a free algebraic framework for analyzing the large N limit of 2D conformal field theories, introducing new algebraic structures and constructions that extend traditional Lie algebra approaches.

Contribution

It introduces an affine free algebra and related free-algebraic structures to describe large N limits of conformal field theories, expanding the mathematical toolkit.

Findings

Derived a new affine free algebra for large N su(N) affine Lie algebra

Constructed free-algebraic partition functions and characters

Developed free-algebraic vertex operator constructions

Abstract

Following recent advances in large N matrix mechanics, I discuss here the free (Cuntz) algebraic formulation of the large N limit of two-dimensional conformal field theories of chiral adjoint fermions and bosons. One of the central results is a new {\it affine free algebra} which describes a large N limit of su(N) affine Lie algebra. Other results include the associated {\it free-algebraic partition functions and characters}, a free-algebraic coset construction, free- algebraic construction of osp(1|2), {\it free-algebraic vertex operator constructions} in the large N Bose systems and a provocative new free-algebraic factorization of the ordinary Koba-Nielsen factor.