CFTs with Large Gap from Barnes-Wall Lattice Orbifolds

TL;DR

This paper constructs a holomorphic conformal field theory with central charge 128 and a large gap by orbifolding Barnes-Wall lattices, proposing a conjecture about anomaly cancellation.

Contribution

It introduces a new method of constructing holomorphic CFTs with large gaps using Barnes-Wall lattice orbifolds and conjectures the vanishing of an anomaly 3-cocycle.

Findings

Constructed a holomorphic CFT of central charge 128 with gap 4.

Proposed a conjecture that the anomaly 3-cocycle vanishes.

Provided evidence supporting the conjecture.

Abstract

We investigate orbifolds of lattice conformal field theories with the goal of constructing theories with large gap. We consider Barnes-Wall lattices, which are a family of lattices with no short vectors, and orbifold by an extraspecial 2-group of lattice automorphisms. To construct the orbifold CFT, we investigate the orbifold vertex operator algebra and its twisted modules. To obtain a holomorphic CFT, a certain anomaly 3-cocycle $\omega$ needs to vanish; based on evidence we provide, we conjecture that it indeed does. Granting this conjecture, we construct a holomorphic CFT of central charge 128 with gap 4.