Area metric gravity à la Plebanski: connection, curvature and dynamics
Abstract
Area metrics arise as effective description at intermediate scales in a number of approaches to quantum gravity, including string theory, holography and loop quantum gravity. Recently, it has been shown that area metric actions can be derived from the modified Plebanski framework on the linearized level. Surprisingly these actions avoid extra poles in the propagator for the effective length dynamics, and hence constitute interesting deformations of linearized Einstein gravity. To be able to study whether this property persist for the full theory, we construct here non-linear area metric dynamics from modified Plebanski actions. We provide the geometric tools for area metrics that do not rely on perturbation theory and allow a systematic construction and study of general non-linear area metric actions: an algorithm that extracts a length metric from an area metric and a connection on two-forms that is uniquely determined by the area metric, together with its curvature and curvature invariants. We derive area metric actions from modified Plebanski actions in first and second order versions. We also find that area metric actions can be reformulated as Poincare gauge theories. We determine the effective length metric action, which on a flat background describes a graviton and a massive spin-two field with parity-violating couplings set by the Barbero--Immirzi parameter. Additionally we discuss cosmological backgrounds and the role of the matter coupling, which together open the way to cosmological applications.
Related
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BibTeX
@misc{dittrich2026area,
title = {{Area metric gravity à la Plebanski: connection, curvature and dynamics}},
author = {Bianca Dittrich},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15838},
eprint = {2610.15838},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15838},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Area metric gravity à la Plebanski: connection, curvature and dynamics
AU - Bianca Dittrich
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15838
UR - https://arxiv.org/abs/2610.15838
AB - Area metrics arise as effective description at intermediate scales in a number of approaches to quantum gravity, including string theory, holography and loop quantum gravity. Recently, it has been shown that area metric actions can be derived from the modified Plebanski framework on the linearized level. Surprisingly these actions avoid extra poles in the propagator for the effective length dynamics, and hence constitute interesting deformations of linearized Einstein gravity. To be able to study whether this property persist for the full theory, we construct here non-linear area metric dynamics from modified Plebanski actions. We provide the geometric tools for area metrics that do not rely on perturbation theory and allow a systematic construction and study of general non-linear area metric actions: an algorithm that extracts a length metric from an area metric and a connection on two-forms that is uniquely determined by the area metric, together with its curvature and curvature invariants. We derive area metric actions from modified Plebanski actions in first and second order versions. We also find that area metric actions can be reformulated as Poincare gauge theories. We determine the effective length metric action, which on a flat background describes a graviton and a massive spin-two field with parity-violating couplings set by the Barbero--Immirzi parameter. Additionally we discuss cosmological backgrounds and the role of the matter coupling, which together open the way to cosmological applications.
ER -