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arXiv 1310.0902hep-th
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超对称Chern-Simons矢量模型中大N热自由能的一个注记

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

Shuichi Yokoyama

摘要:

本文计算了\cN =3 U(N)_k和\cN = 4,6 U(N)_k \times U(N ')_{-k} Chern-Simons理论的精确有效作用量,在“t Hooft”矢量模型极限下,N和k趋于无穷大,保持N/k,N'不变.我们还将此计算推广到\cN = 4,6质量变形的情况。我们证明了除了质量形变\cN =6的情形外,其它大N有效作用量精确地约化为\cN =2 U(N)_k的Chern-Simons理论的作用量.利用这个结果,我们证明了在极限下,包含\cN =4质量项的\cN = 3,4,6 Chern-Simons理论的热自由能和自对偶性约化为\cN =2的情形.

英文摘要:

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.

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