The resolution of field identification fixed points in diagonal coset theories

TL;DR

This paper addresses the fixed point resolution in diagonal coset theories by using automorphism eigenspaces, orbit Lie algebras, and twining characters to compute characters and modular S-matrices, extending to generalized cases.

Contribution

It provides a method to resolve fixed points in diagonal coset theories using eigenspaces, orbit Lie algebras, and twining characters, and expresses the modular S-matrix in terms of these structures.

Findings

Resolved fixed points using eigenspaces of automorphisms.

Expressed characters via branching functions of twining characters.

Connected the modular S-matrix to orbit Lie algebra S-matrices.

Abstract

The fixed point resolution problem is solved for diagonal coset theories. The primary fields into which the fixed points are resolved are described by submodules of the branching spaces, obtained as eigenspaces of the automorphisms that implement field identification. To compute the characters and the modular S-matrix we use `orbit Lie algebras' and `twining characters', which were introduced in a previous paper (hep-th/9506135). The characters of the primary fields are expressed in terms of branching functions of twining characters. This allows us to express the modular S-matrix through the S-matrices of the orbit Lie algebras associated to the identification group. Our results can be extended to the larger class of `generalized diagonal cosets'.