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Congruence Property In Conformal Field Theory

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arxiv 1201.6644 v7 pith:JWWXC2XM submitted 2012-01-31 math.QA hep-thmath-phmath.CTmath.MPmath.RT

Congruence Property In Conformal Field Theory

classification math.QA hep-thmath-phmath.CTmath.MPmath.RT
keywords modularcongruencesubgroupconformalpropertyrepresentationsalgebraanomaly
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Parafermionizing the Monster

    hep-th 2026-05 conditional novelty 7.0

    Assuming a conjectural decomposition of the Monster character, the Monster CFT has Rep(so(3)_p) symmetry for every odd prime p, and the associated defect McKay-Thompson series have invariance subgroup Γ1(p+2).

  2. Parafermionizing the Monster

    hep-th 2026-05 unverdicted novelty 6.0

    Parafermionization equates the Monster CFT to a gauged parafermion pair, yielding Rep(so(3)_p) symmetry and defect McKay-Thompson series invariant under Gamma_1(p+2).

  3. Character Identities Between Affine and Virasoro Vertex Operator Algebra Modules

    math.QA 2025-11 conditional novelty 6.0

    Admissible-level affine sl2 modules and rational Virasoro minimal-model modules have matching characters under the substitution (w,q) -> (q^{+/-1/2}, q^3).