Line Operator Index on S1 $\times$ S3

Understand

We derive a general formula of an index for N = 2 superconformal field theories on S1 \times S3 with insertions of BPS Wilson line or 't Hooft line operator at the north pole and their anti-counterpart at the south pole of S3.

• One-loop and monopole bubbling effects are taken into account in the computation.
• As examples, we calculate the indices for N = 4 theories and N = 2 SU(2) theory with Nf = 4, and find good agreements between indices of line operators related by S-duality.
• The relation between Verlinde loop operators and the indices is explored.