Eta Products, BPS States and K3 Surfaces

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.

45 pages, 5 figures; sections re-ordered and comments added, to appear in JHEP

References in corpus (9)

• Counting Gauge Invariants: the Plethystic Program
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Notes on the K3 Surface and the Mathieu group M_24
• Note on Twisted Elliptic Genus of K3 Surface
• Mathieu Moonshine in the elliptic genus of K3
• Mathieu Moonshine and N=2 String Compactifications
• Mathieu Moonshine and Orbifold K3s
• Graph Zeta Function and Gauge Theories
• Generating spaces of modular forms with $\eta$-quotients

Cited by in corpus (6)

• Twining Genera of (0,4) Supersymmetric Sigma Models on K3
• Sporadic and Exceptional
• Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks
• Hecke Groups, Dessins d'Enfants and the Archimedean Solids
• Exact Half-BPS Black Hole Entropies in CHL Models from Rademacher Series
• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings