False Theta Functions and the Verlinde formula
Quantum Algebra
2014-11-25 v3 High Energy Physics - Theory
Number Theory
Abstract
We discover new analytic properties of classical partial and false theta functions and their potential applications to representation theory of W-algebras and vertex algebras in general. More precisely, motivated by clues from conformal field theory, first, we are able to determine modular-like transformation properties of regularized partial and false theta functions. Then, after suitable identification of regularized partial/false theta functions with the characters of atypical modules for the singlet vertex algebra W(2,2p-1), we formulate and prove a Verlinde-type formula for the fusion rules of irreducible W(2,2p-1)-modules.
Cite
@article{arxiv.1309.6037,
title = {False Theta Functions and the Verlinde formula},
author = {Thomas Creutzig and Antun Milas},
journal= {arXiv preprint arXiv:1309.6037},
year = {2014}
}
Comments
21 pages. v2: a few minor corrections. v3: published version