Holography for tensor models

In this article we explore the holographic duals of tensor models using collective field theory. We develop a description of the gauge invariant variables of the tensor model. This is then used to develop a collective field theory description of the dynamics. We consider matrixlike subsectors that develop an extra holographic dimension. In particular, we develop the collective field theory for the matrixlike sector of an interacting tensor model. We check the correctness of the large $N$ collective field by showing that it reproduces the perturbative expansion of large $N$ expectation values. In contrast to this, we argue that melonic large $N$ limits do not develop an extra dimension. This conclusion follows from the large $N$ value for the melonic collective field, which has delta function support. The finite $N$ physics of the model is also developed and nonperturbative effects in the $1/N$ expansion are exhibited.