Line Operator Index on Sn 1 × Sn 3

摘要

We derive a general formula of an index for ( mathcal{N} = 2 ) superconformal field theories on S1 × 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 ( mathcal{N} = 4 ) theories and ( mathcal{N} = 2 ) SU(2) theory with N f  = 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. The holographic correspondence between the fundamental (anti- symmetric) Wilson line operator and the fundamental string (D5 brane) in AdS5 × S5 is confirmed by the index comparison.