Area-metric gravity revisited

Borissova, Johanna N.; Dittrich, Bianca; Krasnov, Kirill

Abstract

Area metrics are an intriguing generalization of length metrics which the generalization 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 nonlength 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 nonlength degrees of freedom. One of the two parameters determines the strength of parity violations; the other defines a mass parameter for the nonlength 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. In this case the two parameters can be identified with the Barbero-Immirzi parameter and a combination of the Barbero-Immirzi parameter and the Planck mass, respectively. Moreover, we find that area-metric actions in Lorentzian (but not in Euclidean) signature feature wrong-sign kinetic and mass terms for the nonlength 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.

• Journal Article Type: Article
• Acceptance Date: May 13, 2024
• Online Publication Date: Jun 13, 2024
• Publication Date: Jun 12, 2024
• Deposit Date: Jun 20, 2024
• Publicly Available Date: Jun 20, 2024
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 109
• Issue: 12
• Article Number: 124035
• DOI: https://doi.org/10.1103/physrevd.109.124035
• Public URL: https://nottingham-repository.worktribe.com/output/36016264
• Publisher URL: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.109.124035