Tensor Models in d Dimensions (The Quantum Spacetime Seminar Series)

Tensor models define a new large N limit dominated by melonic diagrams. While it seems unlikely that theories with melonic dominance make sense in dimensions greater than 1, it seems important to confirm this by carefully
exploring the range of possibilities for melonic CFT’s, and their relationships to simpler large N theories based on vector or matrix degrees of freedom. In this context we will review some of the work on fermionic and bosonic tensor models in d dimensions over the last year. One positive outcome of these explorations is that it appears possible to study fermionic tensor models in 1 dimension at finite N via an epsilon expansion, starting
from 2-є dimensions.