Toward the construction of the general multi-cut solutions in Chern-Simons matrix models

  • Takeshi MoritaEmail author
  • Kento Sugiyama
Open Access
Regular Article - Theoretical Physics


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.


1/N Expansion Matrix Models Chern-Simons Theories Supersymmetric Gauge Theory 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of PhysicsShizuoka UniversityShizuokaJapan
  2. 2.Graduate School of Science and TechnologyShizuoka UniversityShizuokaJapan

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