Novel construction of boundary states in coset conformal field theories

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× H, we give a map from NIM-reps of G× 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× SU(2) 3/ SU(2) 8 to obtain a new NIM-rep based on the conformal embedding su(2) 3⊕ su(2) 8⊂ sp(6) 1.