Area-metric gravity revisited

TL;DR

This paper explores a class of area-metric gravity theories, identifying conditions for ghost-free gravitons and analyzing their symmetries and stability, with implications for quantum gravity models.

Contribution

It characterizes the space of quadratic, diffeomorphism-invariant area-metric actions, revealing a subclass with enhanced symmetry and stable linearized dynamics.

Findings

A four-parameter family of theories is described.

A two-parameter subclass exhibits shift symmetry and ghost-free gravitons.

Lorentzian signature theories show wrong-sign kinetic terms but remain stable.

Abstract

Area metrics are an intriguing generalization of length metrics which appears in several quantum-gravity approaches. We describe the space of diffeomorphism-invariant area-metric actions quadratic in fluctuations and derivatives. A general theory is found to be specified by four parameters, two of which are mass parameters for the non-length degrees of freedom. We find that a two-parameter subclass of theories exhibits an additional shift symmetry of the kinetic term, and leads to a ghost-free graviton propagator for the effective theory obtained after integrating out the non-length degrees of freedom. One of the two parameters determines the strength of parity violations, the other defines a mass parameter for the non-length degrees of freedom. The same type of action has been found to appear from modified Plebanski theory and in the continuum limit of (effective) spin foams. We moreover find that area-metric actions in Lorentzian (but not in Euclidean) signature feature wrong-sign kinetic and mass terms for the non-length degrees of freedom. Nevertheless, despite a coupling of these degrees of freedom to the length metric, the linearized dynamics turns out to be stable for the above subclass of actions.