Kac-Moody algebras in perturbative string theory

TL;DR

This paper explores the connection between Kac-Moody algebras and perturbative string theory, predicting infinite-dimensional symmetries in Type IIA and IIB strings based on M-theory conjectures and comparing them with string-theoretic constructions.

Contribution

It identifies and compares the predicted Kac-Moody symmetry algebras in string theories with those constructed from string operators, providing evidence for the conjectured symmetries.

Findings

Close agreement between predicted and constructed symmetry algebras

Extension of analysis to bosonic string case

Supports M-theory's conjecture of E11 symmetry

Abstract

The conjecture that M-theory has the rank eleven Kac-Moody symmetry e11 implies that Type IIA and Type IIB string theories in ten dimensions possess certain infinite dimensional perturbative symmetry algebras that we determine. This prediction is compared with the symmetry algebras that can be constructed in perturbative string theory, using the closed string analogues of the DDF operators. Within the limitations of this construction close agreement is found. We also perform the analogous analysis for the case of the closed bosonic string.