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 .
ASJC Scopus subject areas
- Nuclear and High Energy Physics