Fermions Coupled to Emergent Noncommutative Gravity

We study the coupling of fermions to Yang-Mills matrix models in the framework of emergent noncommutative gravity. It is shown that the matrix model action provides an appropriate coupling for fermions to gravity, albeit with a non-standard spin-connection. Integrating out the fermions in a nontrivial geometrical background induces indeed the Einstein-Hilbert action for on-shell geometries plus a dilaton-like term. This result explains UV/IR mixing as a gravity effect. It also illuminates why UV/IR mixing remains even in supersymmetric models, except in the N = 4 case. [email protected], Talk given at the Workshop on Black Holes in General Relativity and String Theory, 24 30 August, 2008, Veli Loŝinj, Croatia. [email protected]