Algebras, BPS States, and Strings

TL;DR

This paper explores the role of BPS states in heterotic string compactifications, revealing their connection to generalized Kac-Moody algebras and proposing a gauge theory reformulation involving hyperbolic algebras.

Contribution

It introduces a new framework linking BPS states to generalized Kac-Moody algebras and suggests a novel reformulation of heterotic strings using hyperbolic algebras.

Findings

Threshold corrections are sums over positive roots of generalized Kac-Moody algebras.

A limit suggests reformulating heterotic string theory with hyperbolic algebras like E10.

Defined a generalized Kac-Moody Lie superalgebra associated with BPS states.

Abstract

We clarify the role played by BPS states in the calculation of threshold corrections of D=4, N=2 heterotic string compactifications. We evaluate these corrections for some classes of compactifications and show that they are sums of logarithmic functions over the positive roots of generalized Kac-Moody algebras. Moreover, a certain limit of the formulae suggests a reformulation of heterotic string in terms of a gauge theory based on hyperbolic algebras such as $E_{10}$. We define a generalized Kac-Moody Lie superalgebra associated to the BPS states. Finally we discuss the relation of our results with string duality.