Modular properties of characters of the W3 algebra
High Energy Physics - Theory
2016-03-01 v3 Quantum Algebra
Abstract
In a previous work, exact formulae and differential equations were found for traces of powers of the zero mode in the W3 algebra. In this paper we investigate their modular properties, in particular we find the exact result for the modular transformations of traces of for n = 1, 2, 3, solving exactly the problem studied approximately by Gaberdiel, Hartman and Jin. We also find modular differential equations satisfied by traces with a single inserted, and relate them to differential equations studied by Mathur et al. We find that, remarkably, these all seem to be related to weight 0 modular forms with expansions with non-negative integer coefficients.
Keywords
Cite
@article{arxiv.1411.4039,
title = {Modular properties of characters of the W3 algebra},
author = {Nicholas J. Iles and Gérard M. T. Watts},
journal= {arXiv preprint arXiv:1411.4039},
year = {2016}
}
Comments
20 pages. v2: 23 pages. v3: 23 pages, published in JHEP