Towards an M5-Brane Model II: Metric String Structures

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.

v2: 70 pages, presentation improved, typos fixed, published version

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• Higher Gauge Theory
• Manifestly Covariant Polynomial M5-brane Lagrangians
• Matrix Quantization of Classical Nambu Brackets and Super $p$-Branes
• Chern correspondence for higher principal bundles
• Explicit Non-Abelian Gerbes with Connections
• $E_2{L}_{\infty }$-algebras, Generalized Geometry, and Tensor Hierarchies
• Adjusting Higher Chern-Simons Theory
• Extended Field Theories as higher Kaluza-Klein theories