Perturbative BPS-algebras in superstring theory

TL;DR

This paper explores the algebraic structure of perturbative BPS-states in superstring theory, revealing connections to generalized Kac-Moody algebras and constructing related Lie-algebras, with applications to orbifold compactifications.

Contribution

It introduces a new Lie-algebra construction with the same graded dimensions as the BPS-algebra, based on a half-twisted model and elliptic genus relations.

Findings

BPS-algebra relates to generalized Kac-Moody algebra in toroidal compactification

Constructed a Lie-algebra with matching graded dimensions using a half-twisted model

Applied the algebraic framework to orbifold compactifications

Abstract

This paper investigates the algebraic structure that exists on perturbative BPS-states in the superstring, compactified on the product of a circle and a Calabi-Yau fourfold. This structure was defined in a recent article by Harvey and Moore. It shown that for a toroidal compactification this algebra is related to a generalized Kac-Moody algebra. The BPS-algebra itself is not a Lie-algebra. However, it turns out to be possible to construct a Lie-algebra with the same graded dimensions, in terms of a half-twisted model. The dimensions of these algebras are related to the elliptic genus of the transverse part of the string algebra. Finally, the construction is applied to an orbifold compactification of the superstring.