A Note on Large N Thermal Free Energy in Supersymmetric Chern-Simons Vector Models

Abstract

We compute the exact effective action for \cN=3 U(N)_k and \cN=4,6 U(N)_k\times U(N')_{-k} Chern-Simons theories with minimal matter content in the 't Hooft vector model limit under which N and k go to infinity holding N/k, N' fixed. We also extend this calculation to \cN=4,6 mass deformed case. We show those large N effective actions except mass-deformed \cN=6 case precisely reduce to that of \cN=2 U(N)_k Chern-Simons theory with one fundamental chiral field up to overall multiple factor. By using this result we argue the thermal free energy and self-duality of the \cN=3,4,6 Chern-Simons theories including the \cN=4 mass term reduce to those of the \cN=2 case under the limit.

27 pages, v2: minor improvements, a reference added, v3: published version

References in corpus (7)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Seiberg Duality in Chern-Simons Theory
• Higher Spins in AdS and Twistorial Holography
• A Massive Study of M2-brane Proposals
• On partition function and Weyl anomaly of conformal higher spin fields
• Chern-Simons-Fermion Vector Model with Chemical Potential

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