Non-Abelian Orbifolds of Lattice Vertex Operator Algebras

2019/09/20 by Gemünden, Thomas, Keller, Christoph A. · 1 citation
#FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1909.09626

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 V^G, and to compute their characters and modular transformation properties. We then construct holomorphic VOAs by adjoining such modules to V^G. 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.

Cited by

• Differential equations for intertwining operators among untwisted and twisted modules

Related

• Orbifolds of Lattice Vertex Operator Algebras at d=48 and d=72
• Orbifolds of Pointed Vertex Operator Algebras I
• On orbifold constructions associated with the Leech lattice vertex operator algebra
• Automorphism groups of cyclic orbifold vertex operator algebras associated with the Leech lattice and some non-prime isometries
• Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices