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 $q$-ensemble describing $U(N)$ 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.

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

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Cited by in corpus (2)

• Complete solution of the LSZ Model via Topological Recursion
• Schur expansion of random-matrix reproducing kernels