Bootstrapping gravity and its extension to metric-affine theories

TL;DR

This paper explores how metric-affine theories of gravity, including torsion and nonmetricity, can be derived via a self-coupling bootstrap approach, clarifying ambiguities and extending to fermions and higher derivatives.

Contribution

It generalizes the self-coupling procedure for metric theories to include torsion, nonmetricity, fermions, and higher derivatives, clarifying previous ambiguities and connecting to Lovelock's theorem.

Findings

Extended the bootstrap method to metric-affine gravity with torsion and nonmetricity.

Clarified ambiguities in defining conserved currents and self-coupling procedures.

Linked the bootstrap ambiguities to Lovelock's theorem.

Abstract

In this work we study diffeomorphism-invariant metric-affine theories of gravity from the point of view of self-interacting field theories on top of Minkowski spacetime (or other background). We revise how standard metric theories couple to their own energy-momentum tensor, and discuss the generalization of these ideas when torsion and nonmetricity are also present. We review the computation of the corresponding currents through the Hilbert and canonical (Noether) prescriptions, emphasizing the potential ambiguities arising from both. We also provide the extension of this consistent self-coupling procedure to the vielbein formalism, so that fermions can be included in the matter sector. In addition, we clarify some subtle issues regarding previous discussions on the self-coupling problem for metric theories, both General Relativity and its higher derivative generalizations. We also suggest a connection between Lovelock theorem and the ambiguities in the bootstrapping procedure arising from those in the definition of conserved currents.