Boundary conditions in charge conjugate sl(N) WZW theories

TL;DR

This paper computes boundary conditions in charge conjugate sl(N) WZW theories by deriving nimreps of the fusion algebra, linking them to classical representation decompositions and modular data of affine B and C algebras.

Contribution

It introduces two methods to compute nimreps for twisted sl(N) WZW theories and relates them to classical algebra decompositions and modular data.

Findings

Derived explicit nimreps for twisted sl(N) WZW boundary conditions.

Connected nimreps to classical representation decompositions.

Expressed nimreps and diagonalisation matrices in terms of affine B and C algebra data.

Abstract

We compute the representations (``nimreps'') of the fusion algebra of affine sl(N), which determine the boundary conditions of sl(N) WZW theories twisted by the charge conjugation. This is done following two procedures, one of general validity, the other specific to the problem at hand. The problem is related to the classical problem of decomposition of the fundamental representations of sl(N) onto representations of $B_l=so(2l+1)$ or $C_l =sp(2l)$ algebras. The relevant nimreps and their diagonalisation matrix are thus expressed in terms of modular data of the affine B or C algebras