1. Non-abelian orbifolds of lattice vertex operator algebras
- Author
-
Thomas Gemünden and Christoph A. Keller
- Subjects
High Energy Physics - Theory ,Vertex (graph theory) ,Pure mathematics ,Holomorphic function ,FOS: Physical sciences ,Vertex operator algebras ,01 natural sciences ,Orbifold Theory ,Mathematics - Quantum Algebra ,0103 physical sciences ,FOS: Mathematics ,Quantum Algebra (math.QA) ,0101 mathematics ,Abelian group ,Mathematical Physics ,Mathematics ,Projective representation ,Algebra and Number Theory ,Conformal packing ,010102 general mathematics ,Mathematical Physics (math-ph) ,Automorphism ,Centralizer and normalizer ,Conformal field theory ,High Energy Physics - Theory (hep-th) ,Operator algebra ,010307 mathematical physics ,Central charge - Abstract
We construct orbifolds of holomorphic lattice vertex operator algebras for non-abelian finite automorphism groups G. To this end, we construct twisted modules for automorphisms g together with the projective representation of the centralizer of g on the twisted module. This allows us to extract the irreducible modules of the fixed-point VOA VG, and to compute their characters and modular transformation properties. We then construct holomorphic VOAs by adjoining such modules to VG. Applying these methods to extremal lattices in d=48 and d=72, we construct more than fifty new holomorphic VOAs of central charge 48 and 72, many of which have a very small number of light states., Journal of Algebra, 585, ISSN:0021-8693, ISSN:1090-266X
- Published
- 2021