Noncommutative D=4 gravity coupled to fermions

Understand

We present a noncommutative extension of Einstein-Hilbert gravity in the context of twist-deformed space-time, with a $\star$-product associated to a quite general triangular Drinfeld twist.

• In particular the $\star$-product can be chosen to be the usual Groenewald-Moyal product.
• The action is geometric, invariant under diffeomorphisms and centrally extended Lorentz $\star$-gauge transformations.
• In the commutative limit it reduces to ordinary gravity, with local Lorentz invariance and usual real vielbein.