A Smooth Model for the String Group

TL;DR

This paper develops a smooth, infinite-dimensional Lie group model for the string group, extends it to a Lie 2-group, and compares different models to establish uniqueness and homotopy properties.

Contribution

It introduces a novel smooth Lie group model for the string group and extends it to a Lie 2-group, providing explicit comparisons and uniqueness results.

Findings

Constructed a smooth infinite-dimensional Lie group model for the string group.

Extended the model to a Lie 2-group with a contractible Lie group.

Provided explicit comparison and a uniqueness theorem for Lie 2-group models.

Abstract

We construct a model for the string group as an infinite-dimensional Lie group. In a second step we extend this model by a contractible Lie group to a Lie 2-group model. To this end we need to establish some facts on the homotopy theory of Lie 2-groups. Moreover, we provide an explicit comparison of string structures for the two models and a uniqueness result for Lie 2-group models.