Oscillatory matrix model in Chern-Simons theory and Jacobi-theta determinantal point process

Abstract

The partition function of the Chern-Simons theory on the three-sphere with the unitary group $U(N)$ provides a one-matrix model. The corresponding $N$-particle system can be mapped to the determinantal point process whose correlation kernel is expressed by using the Stieltjes-Wigert orthogonal polynomials. The matrix model and the point process are regarded as $q$-extensions of the random matrix model in the Gaussian unitary ensemble and its eigenvalue point process, respectively. We prove the convergence of the $N$-particle system to an infinite-dimensional determinantal point process in $N\to \infty$, in which the correlation kernel is expressed by Jacobi's theta functions. We show that the matrix model obtained by this limit realizes the oscillatory matrix model in Chern-Simons theory discussed by de Haro and Tierz.

v2: 29 pages, 5 figures, minor corrections made for publication in J. Math. Phys

References in corpus (3)

• Les Houches lectures on matrix models and topological strings
• Chern-Simons matrix models and Stieltjes-Wigert polynomials
• Noncolliding Brownian Motion with Drift and Time-Dependent Stieltjes-Wigert Determinantal Point Process

Cited by in corpus (4)

• Full counting statistics for interacting trapped fermions
• Torus knot polynomials and susy Wilson loops
• Riemannian Gaussian distributions, random matrix ensembles and diffusion kernels
• The Elliptic Tail Kernel