CFTs with Large Gap from Barnes-Wall Lattice Orbifolds

2024/11/20 by Christoph A. Keller, Keller, Christoph A., Jeremy A. Roberts +2
Computer Science · Mathematics · #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2411.13646

openalex publication_date 2024/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ω 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.

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