Modular invariants and fusion rule automorphisms from Galois theory

Abstract

We show that Galois theory of cyclotomic number fields provides a powerful tool to construct systematically integer-valued matrices commuting with the modular matrix S, as well as automorphisms of the fusion rules. Both of these prescriptions allow the construction of modular invariants and offer new insight in the structure of known exceptional invariants.

11 pages

References in corpus (4)

• Meromorphic c=24 Conformal Field Theories
• The Classification of Affine SU(3) Modular Invariant Partition Functions
• Implications of an arithmetical symmetry of the commutant for modular invariants
• Fusion Algebras Induced by Representations of the Modular Group

Cited by in corpus (8)

• Finite Group Modular Data
• Galois Modular Invariants of WZW Models
• Completeness of boundary conditions for the critical three-state Potts model
• Automorphism Modular Invariants of Current Algebras
• Galois Symmetry Induced by Hecke Relations in Rational Conformal Field Theory and Associated Modular Tensor Categories
• Galois Orbits of TQFTs: Symmetries and Unitarity
• Quasi-Galois Symmetries of the Modular S-Matrix
• Heterotic Modular Invariants and Level--Rank Duality