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Quadratically Extended GR – Leon Menger

Gravity with torsion as deformed BF theory

This paper contains the results of my master thesis under supervision of Alberto Cattaneo and Michele Schiavina. In it we study a family of – possibly non topological –deformations of $BF$ theory for the Lie algebra obtained by quadratic extension (following [1,2]) of $\mathfrak{so}(3,1)$ by an orthogonal module.

The resulting theory – which we called quadratically extended General Relativity (qeGR) – is shown to be classically equivalent to certain models of gravity with dynamical torsion. The classical equivalence is shown to promote to a stronger notion of equivalence within the Batalin–Vilkovisky formalism.

In particular, both Palatini–Cartan gravity and a deformation thereof by a dynamical torsion term, called $(\textit{quadratic})$ generalised Holst theory, are recovered from the standard Batalin–Vilkovisky formulation of qeGR by elimination of generalised auxiliary fields.

The paper is available to read on the arxiv.



Email: info[]leonmenger[]de
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ORCID: 0000000306214977

© Leon Menger 2023

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