Random tensors, melonic theories and quantum gravity

          @misc{ pirsa_PIRSA:20070005,
            doi = {10.48660/20070005},
            url = {https://pirsa.org/20070005},
            author = {Carrozza, Sylvain},
            keywords = {Cosmology, Particle Physics, Quantum Foundations, Quantum Gravity, Quantum Information},
            language = {en},
            title = {Random tensors, melonic theories and quantum gravity},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {jul},
            note = {PIRSA:20070005 see, \url{https://pirsa.org}}
          }
          

Abstract

I will present a brief review of large-N tensor models and their applications in quantum gravity. On the one hand, they provide a general platform to investigate random geometry in an arbitrary number of dimensions, in analogy with the matrix models approach to two-dimensional quantum gravity. Previously known universality classes of random geometries have been identified in this context, with continuous random trees acting as strong attractors. On the other hand, the same combinatorial structure supports a generic family of large-N quantum theories, collectively known as melonic theories. Being largely solvable, they have opened a new window into strongly-coupled quantum theory, and via holography, into quantum gravity. Prime examples are provided by the SYK model and generalizations, which capture essential features of Jackiw-Teitelboim gravity.