Curvature and gravity actions for matrix models

Abstract

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.