Correlators on non-supersymmetric Wilson line in N=4 SYM and AdS${}_2$/CFT${}_1$

Abstract

Correlators of local operators inserted on a straight Wilson loop in a conformal gauge theory have the structure of a one-dimensional "defect" CFT. As was shown in arXiv:1706.00756, in the case of supersymmetric Wilson-Maldacena loop in $\mathcal{N}=4$ SYM one can compute the strong-coupling contributions to 4-point correlators of operator insertions by starting with the AdS${}_5\times S^5$ string action expanded near the AdS${}_2$ minimal surface and evaluating the corresponding AdS${}_2$ Witten diagrams. We perform the analogous computations in the non-supersymmetric case of the standard Wilson loop with no coupling to the scalars. The corresponding non-supersymmetric "defect" CFT${}_1$ has an unbroken $SO(6)$ global symmetry. The elementary bosonic operators (6 SYM scalars and 3 components of the SYM field strength) are dual respectively to the $S^5$ embedding coordinates and AdS${}_5$ coordinates transverse to the minimal surface ending on the line at the boundary. The $SO(6)$ symmetry is preserved provided the 5-sphere coordinates satisfy Neumann boundary conditions (as opposed to Dirichlet in the supersymmetric case); one should then integrate over the $S^5$. The massless $S^5$ fluctuations have logarithmic propagator, corresponding to the boundary scalar operator having dimension $\Delta =\frac{5}{\sqrt{\lambda }}+\dots$ at strong coupling. The resulting functions of 1d cross-ratio in the 4-point functions have a more complicated structure than in the supersymmetric case, involving polylogs (Li${}_3$ and Li${}_2$). We also discuss consistency with the operator product expansion which allows extracting the leading strong coupling corrections to the anomalous dimensions of the operators appearing in the intermediate channels.

50 pages, 12 figures. v2: minor changes

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• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve
• Emitted Radiation and Geometry
• Notes on $n$-point Witten diagrams in AdS${}_2$
• Interpolating Boundary Conditions on $Ad{S}_2$
• Wilson loops in Large Symmetric Representations through a Double-Scaling Limit
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• 1d Conformal Field Theory and Dispersion Relations
• Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories
• Flat limit of massless scalar scattering in ${\mathrm{AdS}}_2$
• Higher order RG flow on the Wilson line in $\mathcal{N}=4$ SYM
• Beyond AdS${}_2$/dCFT${}_1$: Insertions in Two Wilson Loops