Emergence of dynamical tensor fields in composite models of gravity

TL;DR

This paper explores how dynamical tensor fields can emerge in composite gravity models using the functional renormalization group, showing finite kinetic terms develop in the infrared and relate to Einstein-Hilbert structures.

Contribution

It demonstrates the dynamical generation of tensor fields in composite gravity models within the functional renormalization group framework, linking to Einstein-Hilbert structures.

Findings

Finite kinetic terms are generated in the infrared regime.

Agreement with Einstein-Hilbert structure is found in the transverse-traceless sector.

Remaining contributions resemble gauge-fixed Einstein-Hilbert actions.

Abstract

We investigate composite models of gravity and explore how dynamical tensor fields can emerge within the functional renormalization group framework. We consider two prototype models: a fermionic theory and a scalar theory. In both cases, an auxiliary tensor field is introduced via a Hubbard-Stratonovich transformation, corresponding to the composite channel associated with the energy-momentum tensor. We derive the flow equations for the field renormalization factors of the auxiliary tensor field and demonstrate that finite kinetic terms are dynamically generated in the infrared regime. Agreement with the diffeomorphism-invariant quadratic Einstein-Hilbert structure can be established in the transverse-traceless spin-2 sector, while the remaining contributions reside in the longitudinal and trace sectors. Although these terms can be cast into a form reminiscent of gauge-fixed presentations of the quadratic Einstein-Hilbert action, we do not interpret them as originating from a genuine gauge-fixing procedure within the present truncation.