The role of symmetry in the FRGE approach to tensor models

Tim Koslowski (ICN-UNAM)

Matrix models are an extremely useful tool in the description of two-dimensional Euclidean quantum gravity in which pure gravity and gravity coupled to specific matter contents appear as critical points. The FRGE is a useful tool to find these critical points and to estimate the critical exponents. However, for precision calculations of the critical exponents one needs to take the U(N) of the matrix model symmetry into account by solving the corresponding Ward-identity in a self-consistent manner, which indeed leads to rather precise results. The success of matrix models and the discovery of a 1/N expansion has lead to significant interest in colored tensor models as models for quantum gravity in higher dimensions. In the final part of the talk I will discuss the FRGE setup for pure tensor models in three dimensions and first results.