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.

中文翻译：

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具有外部源和Chern-Simons和ABJ（M）类型的q集合的复杂（超级）矩阵模型

Langmann–Szabo–Zarembo（LSZ）矩阵模型是具有四次交互作用和两个外部矩阵的复杂矩阵模型。该模型出现在非交换平面上的标量场理论研究中。我们证明了LSZ矩阵模型计算了Stieltjes-Wigert矩阵模型中非典型波动的概率，该模型可以在三个球面上描述U（N）Chern-Simons理论。对应关系在广义上成立：根据两个外部矩阵的光谱，LSZ矩阵模型要么描述Chern–Simons分区函数中的大波动概率，要么在整齐不变或在两个整齐不变。我们将结果扩展到超级矩阵模型，