Towards an M5-Brane Model II: Metric String Structures

TL;DR

This paper develops a mathematical framework for metric string structures, which are essential in six-dimensional superconformal theories and potentially in formulating the (2,0)-theory, introducing new connections on higher bundles.

Contribution

It introduces the concept of an adjusted Weil algebra for metric string structures, enabling the study of non-abelian gerbe connections beyond traditional limitations.

Findings

Connections on string structures can be non-abelian and interact in new ways.

Derived metric extensions of string structures relevant to supergravity.

Connections match those previously constructed in gauged supergravities.

Abstract

In this paper, we develop the mathematical formulation of metric string structures. These play a crucial role in the formulation of certain six-dimensional superconformal field theories and we believe that they also underlie potential future formulations of the (2,0)-theory. We show that the connections on non-abelian gerbes usually introduced in the literature are problematic in that they are locally gauge equivalent to connections on abelian gerbes. Connections on string structures form an exception and we introduce the general concept of an adjusted Weil algebra leading to potentially interacting connections on higher principal bundles. Considering a special case, we derive the metric extension of string structures and the corresponding adjusted Weil algebra. The latter lead to connections that were previously constructed by hand in the context of gauged supergravities. We also explain how the Leibniz algebras induced by an embedding tensor in gauged supergravities fit into our picture.