Congruence Property In Conformal Field Theory

Understand

The congruence subgroup property is established for the modular representations associated to any modular tensor category.

• This result is used to prove that the kernel of the representation of the modular group on the conformal blocks of any rational, C_2-cofinite vertex operator algebra is a congruence subgroup.
• In particular, the q-character of each irreducible module is a modular function on the same congruence subgroup.
• The Galois symmetry of the modular representations is obtained and the order of the anomaly for those modular categories satisfying some integrality conditions is determined.