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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2602.12312

Authors: Ampagouni, Maneesha, Mason, Geoffrey, Mertens, Michael H.

Institutions: University of California, Santa Cruz, RWTH Aachen University

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: RWTH Aachen University

OpenAlex ID: W7129068049

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