PIRSA:19020038

Video URL

https://pirsa.org/19020038

Tensor models and combinatorics of triangulations in dimensions d>2

Bonzom, V. (2019). Tensor models and combinatorics of triangulations in dimensions d>2. Perimeter Institute for Theoretical Physics. https://pirsa.org/19020038

Bonzom, Valentin. Tensor models and combinatorics of triangulations in dimensions d>2. Perimeter Institute for Theoretical Physics, Feb. 27, 2019, https://pirsa.org/19020038 

          @misc{ scivideos_PIRSA:19020038,
            doi = {10.48660/19020038},
            url = {https://pirsa.org/19020038},
            author = {Bonzom, Valentin},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Tensor models and combinatorics of triangulations in dimensions d>2},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2019},
            month = {feb},
            note = {PIRSA:19020038 see, \url{https://scivideos.org/index.php/pirsa/19020038}}
          }

Valentin Bonzom Gustave Eiffel University

Talk numberPIRSA:19020038
DOI10.48660/19020038
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

Tensor models are generalizations of vector and matrix models. They have been introduced in quantum gravity and are also relevant in the SYK model. I will mostly focus on models with a U(N)^d-invariance where d is the number of indices of the complex tensor, and a special case at d=3 with O(N)^3 invariance. The interactions and observables are then labeled by (d-1)-dimensional triangulations of PL pseudo-manifolds. The main result of this talk is the large N limit of observables corresponding to 2-dimensional planar triangulations at d=3. In particular, models using such observables as interactions have a large N limit exactly solvable as it is Gaussian. If time permits, I will also discuss interesting questions in the field: models which are non-Gaussian at large N, the enumeration of triangulations of PL-manifolds, matrix model representation of some tensor models, etc.