BKM superalgebras from counting dyons in N=4 supersymmetric type II compactifications

TL;DR

This paper explores the algebraic structure of quarter BPS dyon degeneracies in N=4 type II string compactifications, revealing connections to Siegel modular forms, Conway group symmetries, and BKM Lie superalgebras.

Contribution

It introduces new BKM Lie superalgebra structures associated with Z_N orbifolds in type II string theory and links degeneracies to genus-two Siegel modular forms across different string models.

Findings

Degeneracies expressed via genus-two Siegel modular forms.

Construction of BKM Lie superalgebras for Z_N orbifolds.

Identification of Conway group Co_1 in the algebraic structure.

Abstract

We study the degeneracy of quarter BPS dyons in N =4 type II compactifications of string theory. We find that the genus-two Siegel modular forms generating the degeneracies of the quarter BPS dyons in the type II theories can be expressed in terms of the genus-two Siegel modular forms generating the degeneracies of quarter BPS dyons in the CHL theories and the heterotic string. This helps us in understanding the algebra structure underlying the degeneracy of the quarter BPS states. The Conway group, Co_1, plays a role similar to Mathieu group, M_{24}, in the CHL models with eta quotients appearing in the place of eta products. We construct BKM Lie superalgebra structures corresponding to Z_N (for N=2,3,4) orbifolds of the type II string compactified on a six-torus.