Constructs Teichmüller modular forms from holomorphic vertex operator algebras and applies them to connect VOA classification with the geometry of moduli spaces of curves.
The space of graded traces for holomorphic VOAs of small central charge
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abstract
It is one of the remarkable results of vertex operator algebras (VOAs) that the graded traces (one-point correlation functions) of holomorphic VOAs are modular functions. This paper explores the question of which modular functions arise as the graded traces of holomorphic VOAs. For VOAs of small central charge, i.e., $c\le 24$, and a non-zero weight-one subspace, we find that the only conditions imposed on the modular fuctions are those that arise easily out of our condition that the VOAs be of CFT type, that is that they have no negative-weight subspaces and their zero-weight subspace is generated by the vacuum vector.
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2026 1verdicts
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Vertex operator algebras, partition functions and Teichm\"{u}ller modular forms
Constructs Teichmüller modular forms from holomorphic vertex operator algebras and applies them to connect VOA classification with the geometry of moduli spaces of curves.