Vertex algebras and Teichm\'{u}ller modular forms

Autor:	Codogni, Giulio
Rok vydání:	2019
Předmět:	Mathematics - Algebraic Geometry High Energy Physics - Theory Mathematics - Representation Theory 14J15 17B69 (primary) 32G15 14H42 14H10 (secondary)
Druh dokumentu:	Working Paper
Popis:	We associate to any holomorphic vertex algebra a collection of Teichm\"{u}ller modular forms, one in each genus. In genus one we obtain the character of the vertex algebra, and we thus reprove Zhu's modularity result. In higher genus, we prove that these forms have an expansion in terms of the correlation functions of the vertex algebra. We propose applications to the Schottky problem, to the study of the slope of the effective cone of the moduli space of curves, and to the classification of holomorphic vertex algebras. In particular, we prove a uniqueness result for high genera partition functions of the moonshine vertex algebra. Comment: New application to moonshine vertex algebra. A mistake corrected. Clarified the relation with correlation functions
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1901.03079 Zobrazit plný text záznamu View this record from Arxiv