ICTS

Ongoing Work With : Suvankar Dutta(IISER Bhopal), Neetu(IISER Bhopal)
Partition function for Chern-Simons(CS) theory on S^3 (or any Seifert manifold) with a gauge group G and level K can be written as a sum over integrable representations of the corresponding affine Lie algebra of the boundary Wess-Zumino-Witten Model. We consider the partition function for U(N) Chern-Simons theory with level K written as a sum over Integrable representation(for odd K), and show that the restriction over representation dictates a novel phase transition after a particular value of the corresponding ’t Hooft coupling. For small coupling the dominant representations are characterised by Young diagrams with number of boxes on the top-most row being less than the level K. On the other hand after a critical value of the coupling, the dominant representations are always characterised by Young diagrams with exact K number of boxes on the topmost row. This new phase is same in spirit as a no gap phase in the Young diagram side and a cap-gap phase in the eigenvalue side.