Abstract
In our previous work [1], 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.
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Morita, T., Sugiyama, K. Toward the construction of the general multi-cut solutions in Chern-Simons matrix models. J. High Energ. Phys. 2018, 168 (2018). https://doi.org/10.1007/JHEP08(2018)168
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DOI: https://doi.org/10.1007/JHEP08(2018)168