Automorphism group and twisted modules of the twisted Heisenberg-Virasoro vertex operator algebra

TL;DR

This paper determines the automorphism group of a twisted Heisenberg-Virasoro vertex operator algebra, introduces a new Lie algebra for classifying twisted modules, and provides a complete list of irreducible twisted modules.

Contribution

It identifies the automorphism group, constructs a new Lie algebra for module classification, and classifies all irreducible twisted modules for the algebra.

Findings

Automorphism group of the twisted Heisenberg-Virasoro VOA determined.

A new Lie algebra $\\mathcal{L}_t$ introduced for module correspondence.

Complete classification of irreducible twisted modules provided.

Abstract

We first determine the automorphism group of the twisted Heisenberg-Virasoro vertex operator algebra $V_{\mathcal{L}}(\ell_{123},0)$.Then, for any integer $t>1$, we introduce a new Lie algebra $\mathcal{L}_{t}$, and show that $\sigma_{t}$-twisted $V_{\mathcal{L}}(\ell_{123},0)$($\ell_{2}=0$)-modules are in one-to-one correspondence with restricted $\mathcal{L}_{t}$-modules of level $\ell_{13}$, where $\sigma_{t}$ is an order $t$ automorphism of $V_{\mathcal{L}}(\ell_{123},0)$. At the end, we give a complete list of irreducible $\sigma_{t}$-twisted $V_{\mathcal{L}}(\ell_{123},0)$($\ell_{2}=0$)-modules.