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arXiv · 2608.24140

Towards a Connection Formulation of Action-Dependent Palatini Gravity

Callum Bell·David Sloan
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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.

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Callum Bell, David Sloan. 2026-08-25. Towards a Connection Formulation of Action-Dependent Palatini Gravity. https://arxiv.org/abs/2608.24140

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