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

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.

17 pages