String duality, automorphic forms, and generalized Kac-Moody algebras

TL;DR

This paper reviews the connections between string dualities, automorphic forms, and generalized Kac-Moody algebras, highlighting the role of BPS states and their algebraic structures in string compactifications with extended supersymmetry.

Contribution

It synthesizes existing research on the interplay of BPS states, automorphic forms, and algebraic structures in string theory, emphasizing the importance of BPS algebras.

Findings

BPS states relate to automorphic forms in string compactifications.

Automorphic forms encode quantum ground state geometries.

BPS algebras may be central to understanding duality symmetries.

Abstract

This is a summary of a review talk at the Trieste conference on duality symmetries in string theory, April 1997. We review some work that has been done on the relation of BPS states, automorphic forms and the geometry of the quantum ground states of string compactifications with extended supersymmetry, emphasizing the (hypothetically) central role of BPS algebras.