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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.

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Authors and Affiliations

  1. Korea Institute for Advanced Study, Seoul, 130-012, Korea

    Dongmin Gang, Eunkyung Koh & Kimyeong Lee

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  1. Dongmin Gang
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  2. Eunkyung Koh
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  3. Kimyeong Lee
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Correspondence to Dongmin Gang.

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ArXiv ePrint: 1201.5539

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Gang, D., Koh, E. & Lee, K. Line Operator Index on S 1 × S 3 . J. High Energ. Phys. 2012, 7 (2012). https://doi.org/10.1007/JHEP05(2012)007

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