Leibniz-Chern-Simons Theory and Phases of Exceptional Field Theory

Abstract

We discuss a generalization of Chern-Simons theory in three dimensions based on Leibniz (or Loday) algebras, which are generalizations of Lie algebras. Special cases of such theories appear in gauged supergravity, where the Leibniz algebra is defined in terms of the global (Lie) symmetry algebra of the ungauged limit and an embedding tensor. We show that the Leibniz algebra of generalized diffeomorphisms in exceptional field theory can similarly be obtained from a Lie algebra that describes the enhanced symmetry of an `ungauged phase' of the theory. Moreover, we show that a `topological phase' of ${\mathrm{E}}_{8(8)}$ exceptional field theory can be interpreted as a Chern-Simons theory for an algebra unifying the three-dimensional Poincaré algebra and the Leibniz algebra of ${\mathrm{E}}_{8(8)}$ generalized diffeomorphisms.

37 pages, v2: refs. added, minor corrections, version to appear in Comm.Math.Phys

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Cited by in corpus (16)

• The Geometry, Branes and Applications of Exceptional Field Theory
• The Embedding Tensor, Leibniz-Loday Algebras, and Their Higher Gauge Theories
• Non-Riemannian geometry of M-theory
• Leibniz Gauge Theories and Infinity Structures
• Kaluza-Klein reduction on a maximally non-Riemannian space is moduli-free
• Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
• Towards an M5-Brane Model II: Metric String Structures
• The controlling $L_{\infty }$-algebra, cohomology and homotopy of embedding tensors and Lie-Leibniz triples
• Higher Gauge Structures in Double and Exceptional Field Theory
• Infinity-enhancing of Leibniz algebras
• Leibniz-Yang-Mills Gauge Theories and the 2-Higgs Mechanism
• Constructions of L${}_{\infty }$ algebras and their field theory realizations
• Higher curvature Bianchi identities, generalised geometry and $L_{\infty }$ algebras
• $E_2{L}_{\infty }$-algebras, Generalized Geometry, and Tensor Hierarchies
• Dg Loday-Pirashvili modules over Lie algebras
• Exotic Aspects of Extended Field Theories