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

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.

43 pages, 16 figures, v2: published version, minor changes

References in corpus (10)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Notes on SUSY Gauge Theories on Three-Sphere
• Resumming the string perturbation series
• On Large N Solution of Gaiotto-Tomasiello Theory
• Wilson loops in unitary matrix models at finite $N$
• Complex saddles in the Gross-Witten-Wadia matrix model
• Supersymmetric solutions and Borel singularities for N=2 supersymmetric Chern-Simons theories
• Bubbling Calabi-Yau geometry from matrix models
• Emergent Phase Space Description of Unitary Matrix Model
• Phase Transition of Anti-Symmetric Wilson Loops in $\mathcal{N}=4$ SYM

Cited by in corpus (1)

• Chern-Simons Theory on Seifert Manifold and Matrix Model