Higher spin matrix models

We propose a hybrid class of theories for higher spin gravity and matrix models, i.e. which handle simultaneously higher spin gravity fields and matrix models. The construction is similar to Vasiliev's higher spin gravity but part of the equations of motion are provided by the action principle of a matrix model. In particular we construct a higher spin (gravity) matrix model related to type IIB matrix models/string theory which have a well defined classical limit, and which is compatible with higher spin gravity in $AdS$ space. As it has been suggested that higher spin gravity should be related to string theory in a high energy (tensionless) regime, and therefore to M-Theory, we expect that our construction will be useful to explore concrete connections.