Instanton moduli spaces and bases in coset conformal field theory

TL;DR

This paper explores special bases in two-dimensional conformal field theories linked to four-dimensional supersymmetric gauge theories, focusing on their properties, explicit constructions, and differences in specific cases.

Contribution

It provides an explicit construction and analysis of distinguished bases in coset conformal field theories related to U(r) gauge theories on orbifolds, highlighting their unique properties.

Findings

Existence of different bases for p=2, r=2 case

Explicit construction of one basis provided

Proposed formula for matrix elements in another basis

Abstract

Recently proposed relation between conformal field theories in two dimensions and supersymmetric gauge theories in four dimensions predicts the existence of the distinguished basis in the space of local fields in CFT. This basis has a number of remarkable properties, one of them is the complete factorization of the coefficients of the operator product expansion. We consider a particular case of the U(r) gauge theory on C^2/Z_p which corresponds to a certain coset conformal field theory and describe the properties of this basis. We argue that in the case p=2, r=2 there exist different bases. We give an explicit construction of one of them. For another basis we propose the formula for matrix elements.