Exact SUSY Wilson loops on S 3 from q-Virasoro constraints

Abstract

Abstract Using the ideas from the BPS/CFT correspondence, we give an explicit recur- sive formula for computing supersymmetric Wilson loop averages in 3d N $$ \mathcal{N} $$ = 2 Yang-Mills-Chern-Simons U(N) theory on the squashed sphere S b 3 $$ {S}_b^3 $$ with one adjoint chiral and two antichiral fundamental multiplets, for specific values of Chern-Simons level κ 2 and Fayet- Illiopoulos parameter κ 1. For these values of κ 1 and κ 2 the north and south pole turn out to be completely independent, and therefore Wilson loop averages factorize into answers for the two constituent D 2 × S 1 theories. In particular, our formula provides results for the theory on the round sphere when the squashing is removed.

Keywords

• Matrix Models
• Wilson
• ’t Hooft and Polyakov loops
• Chern-Simons Theories
• Supersymmetric Gauge Theory