The Loop Group of E8 and Targets for Spacetime

TL;DR

This paper explores the connection between E8 gauge theory reduction and loop bundles in string theory, proposing a sigma model with E8 target space and analyzing its mathematical structure and potential physical implications.

Contribution

It introduces a novel framework linking E8 gauge theory reduction to loop group bundles and sigma models in string theory.

Findings

Identification of the loop bundle structure in type IA string theory

Proposal of a sigma model with E8 target space

Analysis of flat connections and potential Lagrangians

Abstract

The dimensional reduction of the E8 gauge theory in eleven dimensions leads to a loop bundle in ten dimensional type IA string theory. We show that the restriction to the Neveu-Schwarz sector leads naturally to a sigma model with target space E8 with the ten-dimensional spacetime as the source. The corresponding bundle has a structure group the group of based loops, whose classifying space we study. We explore some consequences of this proposal such as possible Lagrangians and existence of flat connections.