The 1/N Expansion in Random Tensor Models

          @misc{ pirsa_PIRSA:12050055,
            doi = {10.48660/12050055},
            url = {https://pirsa.org/12050055},
            author = {Gurau, Razvan},
            keywords = {},
            language = {en},
            title = {The 1/N Expansion in Random Tensor Models},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {may},
            note = {PIRSA:12050055 see, \url{https://pirsa.org}}
          }
          

Abstract

Matrix models yield a theory of random two dimensional surfaces. They support a 1/N expansion dominated by planar graphs (corresponding to planar surfaces) and undergo a phase transition to a continuum theory. In higher dimensions matrix models generalize to tensor models. In the absence of a viable 1=N expansion, tensor models have for a long time been less successful in providing a theory of random higher dimensional spaces. This situation has drastically changed recently. Models for a non-symmetric complex tensor have been shown to admit a 1/N expansion dominated by graphs of spherical topology in arbitrary dimensions and to undergo a phase transition to a continuum theory. I will present an overview of these results and discuss their implications.