The gauge symmetries of f(R) gravity with torsion in the Cartan formalism

Understand

First-order general relativity in $n$ dimensions ($n \geq 3$) has an internal gauge symmetry that is the higher-dimensional generalization of three-dimensional local translations.

• We report the extension of this symmetry for $n$-dimensional f(R) gravity with torsion in the Cartan formalism.
• The new symmetry arises from the direct application of the converse of Noether's second theorem to the action principle of f(R) gravity with torsion.
• We show that infinitesimal diffeomorphisms can be written as a linear combination of the new internal gauge symmetry, local Lorentz transformations, and terms proportional to the variational derivatives of the f(R) action.