Sakharov's induced gravity and the Poincar\'e gauge theory

TL;DR

This paper investigates Sakharov's idea that gravity emerges from quantum matter corrections, deriving the Poincaré gauge theory of gravity within a Riemann--Cartan framework and linking the induced Newton constant to the Planck scale.

Contribution

It explicitly derives the Poincaré gauge theory of gravity as an induced action from quantum matter fields in a Riemann--Cartan spacetime, extending Sakharov's mechanism.

Findings

Induced Newton constant is of the order of the Planck mass.

Gravity can be viewed as an emergent phenomenon from quantum matter corrections.

The approach applies to gauge theories of gravity at low energies.

Abstract

We explore Sakharov's seminal idea that gravitational dynamics is induced by the quantum corrections from the matter sector. This was the starting point of the view that gravity has an emergent origin, which soon gained impetus due to the advent of black hole thermodynamics. In the generalized framework of Riemann--Cartan spacetime with both curvature and torsion, the induced gravitational action is obtained for free nonminimally coupled scalar and Dirac fields. For a realistic matter content, the induced Newton constant is obtained to be of the magnitude of the ultraviolet cutoff, which implies that the cutoff is of the order of the Planck mass. Finally, we conjecture that the action for any gauge theory of gravity at low energies can be induced by Sakharov's mechanism. This is explicitly shown by obtaining the Poincar\'e gauge theory of gravity.