Curvature and gravity actions for matrix models

We show how gravitational actions, in particular the Einstein-Hilbert action, can be obtained from additional terms in Yang-Mills matrix models. This is consistent with recent results on induced gravitational actions in these matrix models, realizing spacetime as four-dimensional brane solutions. It opens up the possibility for a controlled non-perturbative description of gravity through simple matrix models, with interesting perspectives for the problem of vacuum energy. The relation with UV/IR mixing and non-commutative gauge theory is discussed.