Eta Products, BPS States and K3 Surfaces
High Energy Physics - Theory
2015-06-17 v3 Algebraic Geometry
Number Theory
Abstract
Inspired by the multiplicative nature of the Ramanujan modular discriminant, Delta, we consider physical realizations of certain multiplicative products over the Dedekind eta-function in two parallel directions: the generating function of BPS states in certain heterotic orbifolds and elliptic K3 surfaces associated to congruence subgroups of the modular group. We show that they are, after string duality to type II, the same K3 surfaces admitting Nikulin automorphisms. In due course, we will present some identities arising from q-expansions as well as relations to the sporadic Mathieu group M24.
Cite
@article{arxiv.1308.5233,
title = {Eta Products, BPS States and K3 Surfaces},
author = {Yang-Hui He and John McKay},
journal= {arXiv preprint arXiv:1308.5233},
year = {2015}
}
Comments
45 pages, 5 figures; sections re-ordered and comments added, to appear in JHEP