Line Operator Index on S 1 × S 3

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Abstract

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.

Keywords

Supersymmetric gauge theory Wilson ’t Hooft and Polyakov loops Duality in Gauge Field Theories Nonperturbative Effects 
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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.Korea Institute for Advanced StudySeoulKorea

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