Phases of large N vector Chern-Simons theories on S 2× S 1

Abstract

We study the thermal partition function of level k U (N) Chern-Simons theories on S 2 interacting with matter in the fundamental representation. We work in the’t Hooft limit,, with and held fixed where T is the temperature and V 2 the volume of the sphere. An effective action proposed in arXiv: 1211.4843 relates the partition function to the expectation value of a ‘potential’function of the S 1 holonomy in pure Chern-Simons theory; in several examples we compute the holonomy potential as a function of λ. We use level-rank duality of pure Chern-Simons theory to demonstrate the equality of thermal partition functions of previously conjectured dual pairs of theories as a function of the temperature. We reduce the partition function to a matrix integral over holonomies.