Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories

TL;DR

This paper develops tropical geometry techniques to analyze strong coupling limits in supersymmetric Chern-Simons-matter theories, providing exact spectral curves and matching AdS dual predictions.

Contribution

It introduces a novel tropical geometry approach to extract strong coupling results directly from spectral curves in these theories.

Findings

Strong coupling corresponds to tropical limit of spectral curve

Spectral curve degenerates to a planar graph in this limit

Results agree with AdS dual predictions involving tri-Sasakian manifolds

Abstract

We study various aspects of the matrix models calculating free energies and Wilson loop observables in supersymmetric Chern-Simons-matter theories on the three-sphere. We first develop techniques to extract strong coupling results directly from the spectral curve describing the large N master field. We show that the strong coupling limit of the gauge theory corresponds to the so-called tropical limit of the spectral curve. In this limit, the curve degenerates to a planar graph, and matrix model calculations reduce to elementary line integrals along the graph. As an important physical application of these tropical techniques, we study N=3 theories with fundamental matter, both in the quenched and in the unquenched regimes. We calculate the exact spectral curve in the Veneziano limit, and we evaluate the planar free energy and Wilson loop observables at strong coupling by using tropical geometry. The results are in agreement with the predictions of the AdS duals involving tri-Sasakian manifolds