## Algebra & Number Theory

### Congruence property in conformal field theory

#### Abstract

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, $C2$-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.

#### Article information

Source
Algebra Number Theory, Volume 9, Number 9 (2015), 2121-2166.

Dates
Revised: 20 July 2015
Accepted: 19 August 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.ant/1510842423

Digital Object Identifier
doi:10.2140/ant.2015.9.2121

Mathematical Reviews number (MathSciNet)
MR3435813

Zentralblatt MATH identifier
1377.17025

#### Citation

Dong, Chongying; Lin, Xingjun; Ng, Siu-Hung. Congruence property in conformal field theory. Algebra Number Theory 9 (2015), no. 9, 2121--2166. doi:10.2140/ant.2015.9.2121. https://projecteuclid.org/euclid.ant/1510842423

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