Renormalization Group analysis of the Ising Model on Causal Dynamical Triangulations

The aim of the talk is to analyse the matrix model characterizing two-dimensional Ising model coupled to Causal Dynamical Triangulations (CDT) from the point of view of the Functional Renormalization Group Equation (FRGE). With the purpose of finding possible continuum limits of the theory, we will analyse the FRGE of the dually weighted matrix model which generalises the Benedetti-Henson model for triangulations with a preferred time foliation to include Ising degrees of freedom. In particular, we find the fixed points of the beta-function equations, showing that the number of relevant directions in each case is compatible with the physical interpretation of the CFT living on the fixed points. In addition to recovering the fixed points for topological gravity and pure gravity with a cosmological constant, we find a new fixed point featuring three relevant directions which match the number of primary fields in the Ising CFT.