Description
I will discuss random tensor models for quantum gravity, of a particular case with mixed U(N) and O(D) symmetry.
A certain U(N)^2 \otimes O(D) order-3 tensor model can be viewed as a complex multi-matrix model with D copies of complex matrices. This model admits an expansion in two parameters owing to the presence of N and D, and yields a more refined classification of Feynman graphs generated by the model. Such a refined expansion has piqued our curiosity in the possibility of finding a new universality class for this tensor model. In the end, we obtain universality classes of branched polymers and also the Brownian sphere (Liouville 2-dimensional quantum gravity).
As a dessert, I will also discuss enumerations of invariants for tensors of arbitrary order with mixed unitary and orthogonal symmetry, and unveil correspondence with the topological field theory.
