Congruence property in conformal field theory

Dong, Chongying; Lin, Xingjun; Ng, Siu-Hung

doi:10.2140/ant.2015.9.2121

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-7833 (online)

ISSN 1937-0652 (print)

Author index

To appear

Other MSP journals

Congruence property in conformal field theory

Chongying Dong, Xingjun Lin and Siu-Hung Ng

Vol. 9 (2015), No. 9, 2121–2166

DOI: 10.2140/ant.2015.9.2121

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, $C_{2}$ -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.

Keywords

Frobenius–Schur indicator, modular tensor category, modular group, vertex operator algebra

Mathematical Subject Classification 2010

Primary: 17B69

Secondary: 18D10, 20H05, 81R05

Milestones

Received: 5 March 2015

Revised: 20 July 2015

Accepted: 19 August 2015

Published: 4 November 2015

Authors

Chongying Dong
Department of Mathematics UC Santa Cruz 194 Baskin Engineering Santa Cruz, CA 95064 United States

Xingjun Lin
Department of Mathematics Sichuan University Chengdu, 610064 China

Siu-Hung Ng
Department of Mathematics Louisiana State University Baton Rouge, LA 70803 United States

Vol. 9, No. 9, 2015