Non-Chiral Vertex Operator Algebra Associated To Lorentzian Lattices And Narain CFTs

Abstract

Frenkel, Lepowsky, and Meurman constructed a vertex operator algebra (VOA) associated to any even, integral, Euclidean lattice. In the language of physics, these are examples of chiral conformal field theories (CFT). In this paper, we define non-chiral vertex operator algebra and some associated notions. We then give a construction of a non-chiral VOA associated to an even, integral, Lorentzian lattice and construct their irreducible modules. We obtain the moduli space of such modular invariant non-chiral CFTs based on even, self-dual Lorentzian lattices of signature $(m,n)$ assuming the validity of a technical result about automorphisms of the lattice. We finally show that Narain conformal field theories in physics are examples of non-chiral VOA. Our formalism helps us to identify the chiral algebra of Narain CFTs in terms of a particular sublattice and give us the decomposition of its partition function into sum of characters.

100 Pages, Comments are welcome! v2:minor corrections and clarifications

References in corpus (5)

• Chern-Simons Invariants from Ensemble Averages
• Narain CFTs and Quantum Codes at Higher Genus
• Classification of Unitary RCFTs with Two Primaries and Central Charge Less Than 25
• Holographic description of Narain CFTs and their code-based ensembles
• Meromorphic Cosets and the Classification of Three-Character CFT

Cited by in corpus (2)

• Fermionic CFTs from topological boundaries in abelian Chern-Simons theories
• Beauty And The Beast Part 2: Apprehending The Missing Supercurrent