Balanced root systems and a Schellekens-type list for holomorphic vertex operator algebras of central charge $32$

arXiv (Cornell University)

Abstract

We study a special class of holomorphic vertex operator algebras (VOAs) that we call \emph{balanced}.\ For a balanced, holomorphic VOA $V=\mathbb{C}\mathbf{1}\oplus V_1\oplus\dots$ with $c=32$ or $40$ we show that the Virasoro vectors of $V$ and the subVOA generated by $V_1$ coincide and use this result to provide a Schellekens-type list of possible root systems that may occur.

Authors 3

1. Maneesha Ampagouni

   University of California, Santa Cruz

   Affiliation as printed

   University of California at Santa Cruz

2. Geoffrey Mason

   University of California, Santa Cruz

   Affiliation as printed

   University of California at Santa Cruz

3. Michael H. Mertens Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University