Topological gravity and transgression holography

Abstract

We show that Poincare-invariant topological gravity in even dimensions can be formulated as a transgression field theory in one higher dimension whose gauge connections are associated to linear and nonlinear realizations of the Poincare group ISO(d-1,1). The resulting theory is a gauged WZW model whereby the transition functions relating gauge fields live in the coset ISO(d-1,1)/SO(d-1,1). The coordinate parametrizing the coset space is identified with the scalar field in the adjoint representation of the gauge group of the even-dimensional topological gravity theory. The supersymmetric extension leads to topological supergravity in two dimensions starting from a transgression field theory which is invariant under the supersymmetric extension of the Poincare group in three dimensions. We also apply this construction to a three-dimensional Chern-Simons theory of gravity which is invariant under the Maxwell algebra and obtain the corresponding WZW model.

22 pages; v2: minor corrections, references added; v3: analysis involving Maxwell algebra expanded, references added; v4: referencing fixed; Final version to be published in Physical Review D

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• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Expanding Lie (super)algebras through abelian semigroups
• Generalized cosmological term from Maxwell symmetries
• The Extended Cartan Homotopy Formula and a Subspace Separation Method for Chern--Simons Theory
• General Relativity from a gauged WZW term
• The Universe as a topological defect
• Topological gravity and Wess-Zumino-Witten term

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