VEVs of Wilson loops in Chern-Simons theory with compact gauge groups give us colored Jones, HOMFLY and Kauffman polynomials. I have not seen the computation for Wilson loops in Chern-Simons theory with non-compact gauge groups. I think that what keep us from computing them is due to infinite dimensional representations of non-compact gauge groups.
Are there any references which describe this problem explicitly? What are the issues in computing Wilson loops in non-compact gauge groups? Is there any proposal to calculate them? Especially I am interested in the simplest cases of $SL(2,R)$ and $SL(2,C)$.
