Towards a Connection Formulation of Action-Dependent Palatini Gravity
Abstract
Previous work has shown that first-order Palatini gravity may be cast as a non-conservative Herglotz Lagrangian field theory, which excludes the conformal mode from its space of dynamical variables. In the present work, we analyse the role of the SO(1,3) gauge connection in the construction of this action-dependent theory. The connection may be algebraically decomposed into complementary sectors which we interpret as `shape' and `scale' components. Only the former is retained within the Herglotz theory, while the latter is incorporated into the action-dependent sector. It is shown that the choice of connection decomposition is a space that can be smoothly parameterised. Such an observation leads to the finding that there exists a `moduli space of frictional field theories', in which each point corresponds to a distinct algebraic splitting of the connection into shape and scale pieces. Movement within the moduli space transitions between Herglotz Lagrangians whose on-shell dynamics all reproduce first-order Palatini gravity. The distinction lies in how the reproduction of the scale dynamics of the original theory is partitioned between action dependence and dynamical torsion.
Related
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BibTeX
@misc{bell2026towards,
title = {{Towards a Connection Formulation of Action-Dependent Palatini Gravity}},
author = {Callum Bell and David Sloan},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.24140},
eprint = {2608.24140},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.24140},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Towards a Connection Formulation of Action-Dependent Palatini Gravity
AU - Callum Bell
AU - David Sloan
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.24140
UR - https://arxiv.org/abs/2608.24140
AB - Previous work has shown that first-order Palatini gravity may be cast as a non-conservative Herglotz Lagrangian field theory, which excludes the conformal mode from its space of dynamical variables. In the present work, we analyse the role of the SO(1,3) gauge connection in the construction of this action-dependent theory. The connection may be algebraically decomposed into complementary sectors which we interpret as `shape' and `scale' components. Only the former is retained within the Herglotz theory, while the latter is incorporated into the action-dependent sector. It is shown that the choice of connection decomposition is a space that can be smoothly parameterised. Such an observation leads to the finding that there exists a `moduli space of frictional field theories', in which each point corresponds to a distinct algebraic splitting of the connection into shape and scale pieces. Movement within the moduli space transitions between Herglotz Lagrangians whose on-shell dynamics all reproduce first-order Palatini gravity. The distinction lies in how the reproduction of the scale dynamics of the original theory is partitioned between action dependence and dynamical torsion.
ER -