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arXiv · 1401.3653

Topological gravity and transgression holography

Patricio Salgado·Richard J. Szabo·Omar Valdivia
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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.

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Patricio Salgado, Richard J. Szabo, Omar Valdivia. 2014-04-14. Topological gravity and transgression holography. https://doi.org/10.1103/physrevd.89.084077

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