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We consider 3+1-dimensional gauge theories at finite temperature and a finitedensity of charges which couple to a 2+1-dimensional Chern-Simons operator,giving rise to a theta-term with constant spatial gradient of theta. Thestrong-coupling limit of thermal N=4 super-Yang-Mills theory with this kind ofanisotropic deformation has been used in the context of the AdS/CFTcorrespondence as a model for strongly coupled anisotropic quark-gluon plasma.In this paper we work out the thermodynamics and the (nontrivial) phase diagramin the limit of vanishing gauge coupling and compare with the correspondingstrong-coupling results.

Thermodynamics and phase diagram of anisotropic Chern-Simons deformed gauge theories