Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-11-29
Physics
High Energy Physics
High Energy Physics - Theory
32 pages, 7 figures. v2: small corrections, added an Appendix on the relation with the approach of 1011.5487. v3: further corr
Scientific paper
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
Marino Marcos
Putrov Pavel
Santamaria Ricardo Couso
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