Higher Gauge Structures in Double and Exceptional Field Theory

Abstract

We review the higher gauge symmetries in double and exceptional field theory from the viewpoint of an embedding tensor construction. This is based on a (typically infinite-dimensional) Lie algebra $\mathfrak{g}$ and a choice of representation $R$. The embedding tensor is a map from the representation space $R$ into $\mathfrak{g}$ satisfying a compatibility condition (`quadratic constraint'). The Lie algebra structure on $\mathfrak{g}$ is transported to a Leibniz--Loday algebra on $R$, which in turn gives rise to an $L_{\infty }$-structure. We review how the gauge structures of double and exceptional field theory fit into this framework.

18 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018

References in corpus (9)

• Double Field Theory
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• Exceptional Field Theory III: E${}_{8(8)}$
• Generalized E(7(7)) coset dynamics and D=11 supergravity
• Supersymmetric E${}_{7(7)}$ Exceptional Field Theory
• Tensor Hierarchy and Generalized Cartan Calculus in SL(3)$\times$SL(2) Exceptional Field Theory
• The Embedding Tensor, Leibniz-Loday Algebras, and Their Higher Gauge Theories
• Leibniz-Chern-Simons Theory and Phases of Exceptional Field Theory

Cited by in corpus (11)

• The Embedding Tensor, Leibniz-Loday Algebras, and Their Higher Gauge Theories
• Leibniz Gauge Theories and Infinity Structures
• Leibniz-Chern-Simons Theory and Phases of Exceptional Field Theory
• Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
• Global Double Field Theory is Higher Kaluza-Klein Theory
• From Lie algebra crossed modules to tensor hierarchies
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Higher curvature Bianchi identities, generalised geometry and $L_{\infty }$ algebras
• The puzzle of global Double Field Theory: open problems and the case for a Higher Kaluza-Klein perspective
• The many facets of exceptional field theory
• Extended Field Theories as higher Kaluza-Klein theories