Galois currents and the projective kernel in rational conformal field theory

2003/03/04 by P. Bantay, Peter Bantay
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Conformal field theory #Differential Galois theory #Embedding problem #Fundamental theorem of Galois theory #Galois extension #Galois group #Galois theory #Homotopy and Cohomology in Algebraic Topology #Kernel (algebra) #Scalar (mathematics) #hep-th #math.QA

paper · pdf · doi:10.1088/1126-6708/2003/03/025

published as JHEP 0303 (2003) 025

arxiv created 2003/03/04 · openalex publication_date 2003/03/13 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The notion of Galois currents in Rational Conformal Field Theory is introduced and illustrated on simple examples. This leads to a natural partition of all theories into two classes, depending on the existence of a non-trivial Galois current. As an application, the projective kernel of a RCFT, i.e. the set of all modular transformations represented by scalar multiples of the identity, is described in terms of a small set of easily computable invariants.

Citations

• Modular invariance and uniqueness of conformal characters
• Comments on the links between su(3) modular invariants, simple factors in the Jacobian of Fermat curves, and rational triangular billiards
• On the classification of modular fusion algebras
• Classical and quantum conformal field theory