Symmetry algebra in gauge theories of gravity

Abstract

Diffeomorphisms and an internal symmetry (e.g., local Lorentz invariance) are typically regarded as the symmetries of any geometrical gravity theory, including general relativity. In the first-order formalism, diffeomorphisms can be thought of as a derived symmetry from the so-called local translations, which have improved properties. In this work, the algebra of an arbitrary internal symmetry and the local translations is obtained for a generic gauge theory of gravity, in any spacetime dimensions, and coupled to matter fields. It is shown that this algebra closes off shell suggesting that these symmetries form a larger gauge symmetry. In addition, a mechanism to find the symmetries of theories that have nondynamical fields is proposed. It turns out that the explicit form of the local translations depend on the internal symmetry and that the algebra of local translations and the internal group still closes off shell. As an example, the unimodular Einstein-Cartan theory in four spacetime dimensions, which is only invariant under volume preserving diffeomorphisms, is studied.

14 pages, improved version

References in corpus (6)

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• Spontaneous and Explicit Spacetime Symmetry Breaking in Einstein-Cartan Theory with Background Fields
• Off-shell Noether currents and potentials for first-order general relativity
• Are inertial vacua equivalent in Lorentz-violating theories? Does it matter?
• Unimodular gravity as an initial value problem
• Revisiting cosmological diffusion models in Unimodular Gravity and the $H_0$ tension
• On the unexpected geometrical origin of the algebra of symmetries
• Semiclassical Gravity Beyond General Relativity: Insights from Torsion