Exploring continuum limits of random tesnor models for quantum gravity with the functional renormalization group equation
The Feynman graphs of (un)colored random tensor models possess a dual interpretation as dicrete random geometries. Using this dual interpretation, one can translate the Feynman amplitude into a Boltzmann factor for each geometry. This translates the partition function of random tensor models into a partition function for discrete quantum gravity. To make a connection with continuum quantum gravity one has to consider critical point of this partition function, where the expectation value of the number of discrete building blocks diverges in a controled way, such that one can interpret the Feynman diagrams as infinitely fine tesselations of geometry. This scaling requires the simultaneous limit of taking the tensor size N to infinity and the scaling the tensor coupling constant to its critical value with the correct critical exponent. The continuum limit of quantum gravity is thus related to critical points of the random tensor model and can thus be investigated with the renormalization group flow in the tensor size N. I will present the general setup for this approach and benchmark tests in 2D Euclidean quantum gravity before explaining the general picture in higher dimesnions. I will cover some results that I obtained in collaboration with Astrid Eichhorn, Antonio Perreira, Johannes Lumma, Joseph Ben Geloun, Daniele Oriti and Alicia Castro and conclude with an outlook to a work program necessary for investigating the possible continuum limits for 4D quantum gravity.