Novel construction of boundary states in coset conformal field theories

TL;DR

This paper introduces a systematic method to construct boundary states in coset conformal field theories by mapping NIM-reps from tensor product theories, leading to new solutions including non-factorizable cases.

Contribution

It provides a novel map from NIM-reps of G x H to those of G/H, expanding the class of known boundary states in coset CFTs.

Findings

Developed a systematic method for solving the Cardy condition in coset theories.

Constructed new NIM-reps, including non-factorizable ones, using simple current actions.

Applied the method to a specific SU(2) coset to find a new NIM-rep based on conformal embedding.

Abstract

We develop a systematic method to solve the Cardy condition for the coset conformal field theory G/H. The problem is equivalent to finding a non-negative integer valued matrix representation (NIM-rep) of the fusion algebra. Based on the relation of the G/H theory with the tensor product theory G x H, we give a map from NIM-reps of G x H to those of G/H. Our map provides a large class of NIM-reps in coset theories. In particular, we give some examples of NIM-reps not factorizable into the G and the H sectors. The action of the simple currents on NIM-reps plays an essential role in our construction. As an illustration of our procedure, we consider the diagonal coset SU(2)_5 x SU(2)_3 /SU(2)_8 to obtain a new NIM-rep based on the conformal embedding su(2)_3 \oplus su(2)_8 \subset sp(6)_1.