Tensor Models and Holography

Knot, matrix and tensor models...melon or meron?

9 févr. 2023, 09:30

1h

Amphithéâtre Hermite (Institut Henri Poincaré)

Orateur

Shinobu Hikami (OIST)

Description

The Gaussian mean of $N\times N$ Hermitian matrix provides a knot configuration
in the replica limit N to 0 (arXiv:2301.06003). The classical knot is related to
Chern-Simons gauge theory, which shows two edges
of Seifert surface are bounded, similar to two merons bounded into instanton.
Higher dimensional knot (2-knot) consists of double Chern-Simons gauge field, which leads to Regge 6-j symbols
tensor model for 3d gravity. We discuss the relation between the intersection numbers of p-spin curves and the quantum knots.
The 4 dimensional Chern-Simons N=2 Yang Mills has an instanton, described by Nekrasov integral, which is akin to the replica formula for the intersection theory.