Toward the construction of the general multi-cut solutions in Chern-Simons Matrix Models

TL;DR

This paper develops an ansatz to analytically construct multi-cut solutions in Chern-Simons matrix models, including ABJM, linking these solutions to D2-brane instantons and extending beyond previous numerical results.

Contribution

It introduces a new ansatz for deriving analytic multi-cut solutions in Chern-Simons matrix models, advancing understanding of their structure and instanton connections.

Findings

Derived novel analytic solutions in pure CS and ABJM models

Established a connection between multi-cut solutions and D2-brane instantons

Extended the solution space beyond previous numerical methods

Abstract

In our previous work arXiv:1704.08675, we pointed out that various multi-cut solutions exist in the Chern-Simons (CS) matrix models at large-$N$ due to a curious structure of the saddle point equations. In the ABJM matrix model, these multi-cut solutions might be regarded as the condensations of the D2-brane instantons. However many of these multi-cut solutions including the ones corresponding to the condensations of the D2-brane instantons were obtained numerically only. In the current work, we propose an ansatz for the multi-cut solutions which may allow us to derive the analytic expressions for all these solutions. As a demonstration, we derive several novel analytic solutions in the pure CS matrix model and the ABJM matrix model. We also develop the argument for the connection to the instantons.