Algebra & Number Theory
- Algebra Number Theory
- Volume 9, Number 9 (2015), 2121-2166.
Congruence property in conformal field theory
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, -cofinite vertex operator algebra is a congruence subgroup. In particular, the -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.
Algebra Number Theory, Volume 9, Number 9 (2015), 2121-2166.
Received: 5 March 2015
Revised: 20 July 2015
Accepted: 19 August 2015
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 17B69: Vertex operators; vertex operator algebras and related structures
Secondary: 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23] 20H05: Unimodular groups, congruence subgroups [See also 11F06, 19B37, 22E40, 51F20] 81R05: Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70]
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