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 $\Delta= \frac{5}{\sqrt\lambda} + \ldots$ 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.