Galois Symmetry Induced by Hecke Relations in Rational Conformal Field Theory and Associated Modular Tensor Categories

Abstract

Hecke operators relate characters of rational conformal field theories (RCFTs) with different central charges, and extend the previously studied Galois symmetry of modular representations and fusion algebras. We show that the conductor $N$ of a RCFT and the quadratic residues mod $N$ play an important role in the computation and classification of Galois permutations. We establish a field correspondence in different theories through the picture of effective central charge, which combines Galois inner automorphisms and the structure of simple currents. We then make a first attempt to extend Hecke operators to the full data of modular tensor categories. The Galois symmetry encountered in the modular data appears in the fusion and the braiding matrices as well, and yields isomorphic structures in theories related by Hecke operators.

v3: editing with referee's response

References in corpus (4)

• Microscopic models of interacting Yang-Lee anyons
• 3-Dimensional TQFTs From Non-Semisimple Modular Categories
• Conformal Field Theories with Sporadic Group Symmetry
• On classification of extremal non-holomorphic conformal field theories

Cited by in corpus (13)

• Higher central charges and topological boundaries in 2+1-dimensional TQFTs
• Holomorphic modular bootstrap revisited
• Rational CFT With Three Characters: The Quasi-Character Approach
• Classifying three-character RCFTs with Wronskian Index equalling $0$ or $2$
• Classification of Unitary RCFTs with Two Primaries and Central Charge Less Than 25
• Wronskian Indices and Rational Conformal Field Theories
• Hecke Relations, Cosets and the Classification of 2d RCFTs
• Galois Orbits of TQFTs: Symmetries and Unitarity
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Two approaches to the holomorphic modular bootstrap
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• Quasi-Characters in $\widehat{su(2)}$ Current Algebra at Fractional Levels
• A Passion for Theoretical Physics: a special issue in memory of Peter G. O. Freund