A Note on Large N Thermal Free Energy in Supersymmetric Chern-Simons Vector Models
Abstract
We compute the exact effective action for =3 U(N)k and =4,6 U(N)k× 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 =4,6 mass deformed case. We show those large N effective actions except mass-deformed =6 case precisely reduce to that of =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 =3,4,6 Chern-Simons theories including the =4 mass term reduce to those of the =2 case under the limit.
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