2017/04/04 by Romo, Mauricio
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1704.00933
We review some recent developments in Chern-Simons theory on a hyperbolic 3-manifold M with complex gauge group G. We focus on the case G=SL(N,ℂ) and with M a knot complement. The main result presented in this note is the cluster partition function, a computational tool that uses cluster algebra techniques to evaluate the Chern-Simons path integral. We also review various applications and open questions regarding the cluster partition function and some of its relation with string theory.