Complex (super)-matrix models with external sources and $q$-ensembles of Chern-Simons and ABJ(M) type
Abstract
The Langmann-Szabo-Zarembo (LSZ) matrix model is a complex matrix model with a quartic interaction and two external matrices. The model appears in the study of a scalar field theory on the non-commutative plane. We prove that the LSZ matrix model computes the probability of atypically large fluctuations in the Stieltjes-Wigert matrix model, which is a -ensemble describing Chern-Simons theory on the three-sphere. The correspondence holds in a generalized sense: depending on the spectra of the two external matrices, the LSZ matrix model either describes probabilities of large fluctuations in the Chern-Simons partition function, in the unknot invariant or in the two-unknot invariant. We extend the result to supermatrix models, and show that a generalized LSZ supermatrix model describes the probability of atypically large fluctuations in the ABJ(M) matrix model.
Keywords
Cite
@article{arxiv.1805.10543,
title = {Complex (super)-matrix models with external sources and $q$-ensembles of Chern-Simons and ABJ(M) type},
author = {Leonardo Santilli and Miguel Tierz},
journal= {arXiv preprint arXiv:1805.10543},
year = {2020}
}
Comments
30 pages, 2 figures. v2: A correction made and several new results added; title changed. v3: Presentation reorganized, new results and references added, final version