Flowing to the continuum limit in tensor models for quantum gravity

Abstract

Tensor models provide a way to access the path-integral for discretized quantum gravity in $d$ dimensions. As in the case of matrix models for 2-dimensional quantum gravity, the continuum limit can be related to a Renormalization Group fixed point in a setup where the tensor size $N$ serves as the Renormalization Group scale. We develop functional Renormalization Group tools for tensor models with a main focus on a rank-3 model for 3-dimensional quantum gravity. We rediscover the double-scaling limit and provide an estimate for the scaling exponent. Moreover, we identify two additional fixed points with a second relevant direction in a truncation of the Renormalization Group flow. The new relevant direction might hint at the presence of additional degrees of freedom in the corresponding continuum limit.