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Exact correlators on the Wilson loop in $$ \mathcal{N}=4 $$ SYM: localization, defect CFT, and integrability

Author(s): Giombi, Simone; Komatsu, Shota

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Abstract: <jats:title>A<jats:sc>bstract</jats:sc> </jats:title> <jats:p>We compute a set of correlation functions of operator insertions on the 1<jats:italic>/</jats:italic>8 BPS Wilson loop in <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$ \mathcal{N}=4 $$</jats:tex-math> <mml:math xmlns:mml=""> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:math> </jats:alternatives> </jats:inline-formula> SYM by employing supersymmetric localization, OPE and the Gram-Schmidt orthogonalization. These correlators exhibit a simple determinant structure, are position-independent and form a topological subsector, but depend nontrivially on the ’t Hooft coupling and the rank of the gauge group. When applied to the 1<jats:italic>/</jats:italic>2 BPS circular (or straight) Wilson loop, our results provide an infinite family of exact defect CFT data, including the structure constants of protected defect primaries of arbitrary length inserted on the loop. At strong coupling, we show precise agreement with a direct calculation using perturbation theory around the AdS<jats:sub>2</jats:sub> string worldsheet. We also explain the connection of our results to the “generalized Bremsstrahlung functions” previously computed from integrability techniques, reproducing the known results in the planar limit as well as obtaining their finite <jats:italic>N</jats:italic> generalization. Furthermore, we show that the correlators at large <jats:italic>N</jats:italic> can be recast as simple integrals of products of polynomials (known as <jats:italic>Q</jats:italic>-functions) that appear in the Quantum Spectral Curve approach. This suggests an interesting interplay between localization, defect CFT and integrability.</jats:p>
Publication Date: 16-May-2018
Electronic Publication Date: 16-May-2018
Citation: Giombi, Simone, Komatsu, Shota. (2018). Exact correlators on the Wilson loop in $$ \mathcal{N}=4 $$ SYM: localization, defect CFT, and integrability. Journal of High Energy Physics, 2018 (5), 10.1007/jhep05(2018)109
DOI: doi:10.1007/jhep05(2018)109
EISSN: 1029-8479
Keywords: AdS-CFT Correspondence, Conformal Field Theory, Supersymmetric Gauge Theory, Wilson, ’t Hooft and Polyakov loops
Language: en
Type of Material: Journal Article
Journal/Proceeding Title: Journal of High Energy Physics
Version: Final published version. This is an open access article.

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