Line Operator Index on S1 $\times$ S3

TL;DR

This paper derives a formula for the superconformal index of N=2 theories on S1×S3 with line operator insertions, incorporating quantum effects, and verifies dualities and holographic relations through explicit calculations.

Contribution

It provides a general formula for line operator indices in N=2 superconformal theories on S1×S3, including quantum corrections, and explores their dualities and holographic correspondences.

Findings

Indices match for S-dual line operators.

Confirmed holographic correspondence with string and D-brane descriptions.

Explicit calculations for N=4 and N=2 theories validate the formula.

Abstract

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. The holographic correspondence between the fundamental (anti-symmetric) Wilson line operator and the fundamental string (D5 brane) in AdS5\timesS5 is confirmed by the index comparison.