Title: String theory, random tensors and combinatoric constructibility (slides)

Speaker: Sanjaye Ramgoolam (QMUL)

Time: 14:00-14:35 (GMT+0), 2021.08.10

Abstract:

Random matrix theories and their tensor generalizations, play a central role in gauge-string dualities such as the AdS/CFT correspondence and simpler mathematical models of the correspondence. Belyi maps, of interest in number theory, describe the geometry of string world-sheets in these simple models of gauge-string duality. I will outline links between the combinatorics of Belyi maps (equivalently of bi-partite ribbon graphs) and matrix as well as tensor models. A Fourier transformation of the combinatorics, which is useful in the study of tensor model correlators, involves linear combinations of bipartite ribbon graphs labelled by triples of Young diagrams and Kronecker coefficient multiplicities. This leads to a combinatoric construction of Kronecker coefficients in terms of lattices of bi-partite ribbon graphs. Another example of combinatoric constructibility in string theory gives the dimensions of irreducible representations of a general finite group in terms of group multiplications shaped according to the fundamental groups of two-dimensional surfaces. The talk is based on https://arxiv.org/abs/2010.04054 and https://arxiv.org/abs/2106.05598.