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Cattaneo, Alberto S.; Menger, Leon; Schiavina, Michele

Gravity with torsion as deformed \(BF\) theory. (English) Zbl 07882225

Classical Quantum Gravity 41, No. 15, Article ID 155001, 59 p. (2024).
Summary: We study a family of (possibly non topological) deformations of \(BF\) theory for the Lie algebra obtained by quadratic extension of \(\mathfrak{so}(3, 1)\) by an orthogonal module. The resulting theory, 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 [[I. A. Batalin and G. A. Vilkovisky, Phys. Lett. B 69, No. 3, 309–312 (1977; 10.1016/0370-2693(77)90553-6 )]. In particular, both Palatini-Cartan gravity and a deformation thereof by a dynamical torsion term, called (quadratic) generalised Holst theory, are recovered from the standard Batalin-Vilkovisky formulation of qeGR by elimination of generalised auxiliary fields.
{© 2024 The Author(s). Published by IOP Publishing Ltd}

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories

Keywords:

BF theory; Batalin-Vilkovisky formalism; torsion; Palatini formalism
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