Reformulation of the symmetries of first-order general relativity

Understand

We report a new internal gauge symmetry of the n-dimensional Palatini action with cosmological term (n>3) that is the generalization of three-dimensional local translations.

• This symmetry is obtained through the direct application of the converse of Noether's second theorem on the theory under consideration.
• We show that diffeomorphisms can be expressed as linear combinations of it and local Lorentz transformations with field-dependent parameters up to terms involving the variational derivatives of the action.
• As a result, the new internal symmetry together with local Lorentz transformations can be adopted as the fundamental gauge symmetries of general relativity.