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Correlators of local operators inserted on a straight Wilson loop in aconformal gauge theory have the structure of a one-dimensional "defect" CFT. Aswas shown in arXiv:1706.00756, in the case of supersymmetric Wilson-Maldacenaloop in $\mathcal{N}=4$ SYM one can compute the strong-coupling contributionsto 4-point correlators of operator insertions by starting with the AdS$_5\times S^5$ string action expanded near the AdS$_2$ minimal surface andevaluating the corresponding AdS$_2$ Witten diagrams. We perform the analogouscomputations in the non-supersymmetric case of the standard Wilson loop with nocoupling to the scalars. The corresponding non-supersymmetric "defect" CFT$_1$has an unbroken $SO(6)$ global symmetry. The elementary bosonic operators (6SYM scalars and 3 components of the SYM field strength) are dual respectivelyto the $S^5$ embedding coordinates and AdS$_5$ coordinates transverse to theminimal surface ending on the line at the boundary. The $SO(6)$ symmetry ispreserved provided the 5-sphere coordinates satisfy Neumann boundary conditions(as opposed to Dirichlet in the supersymmetric case); one should then integrateover the $S^5$. The massless $S^5$ fluctuations have logarithmic propagator,corresponding to the boundary scalar operator having dimension $\Delta=\frac{5}{\sqrt\lambda} + \ldots$ at strong coupling. The resulting functions of1d cross-ratio in the 4-point functions have a more complicated structure thanin the supersymmetric case, involving polylogs (Li$_3$ and Li$_2$). We alsodiscuss consistency with the operator product expansion which allows extractingthe leading strong coupling corrections to the anomalous dimensions of theoperators appearing in the intermediate channels.

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