The Holst Action by the Spectral Action Principle

TL;DR

This paper explores how the Holst action, important in quantum gravity, can be derived from spectral geometry techniques on certain 4-manifolds with specific connection properties.

Contribution

It demonstrates that the Holst action can be obtained from heat asymptotics of the Dirac operator for connections with torsion of zero Cartan type.

Findings

Holst action recovered from heat asymptotics

Applicable to 4-manifolds with orthogonal connections

Connects spectral geometry with gravitational action

Abstract

We investigate the Holst action for closed Riemannian 4-manifolds with orthogonal connections. For connections whose torsion has zero Cartan type component we show that the Holst action can be recovered from the heat asymptotics for the natural Dirac operator acting on left-handed spinor fields.