Novel construction of boundary states in coset conformal field theories
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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.
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Cited by 2 Pith papers
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Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
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Extending fusion rules with finite subgroups: A general construction of $Z_{N}$ extended conformal field theories and their orbifoldings
Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.
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