Notes on Planar Resolvents of Chern-Simons-matter Matrix Models

Abstract

We revisit planar resolvents of matrix models corresponding to $\mathcal{N}\ge 3$ Chern-Simons-matter theories with the gauge groups of the form $\mathrm{U}(N_1)\times \mathrm{U}(N_2)$ coupled to any number of bi-fundamental hypermultiplets. We find that the derivative of a suitably defined planar resolvent can be written explicitly. From this resolvent, we derive the explicit formula for (a linear combination of) the vevs of BPS Wilson loops.

16 pages, v2: perturbative checks for the resolvents added

References in corpus (3)

• Summing Up All Genus Free Energy of ABJM Matrix Model
• Wilson Loops in Superconformal Chern-Simons Theory and Fundamental Strings in Anti-de Sitter Supergravity Dual
• A review on SUSY gauge theories on $S^3$

Cited by in corpus (1)

• Cubic constraints for the resolvents of the ABJM matrix model and its cousins