Correlators on non-supersymmetric Wilson line in $\mathcal{N}=4$ SYM and AdS₂/CFT₁

Abstract

Correlators of local operators inserted on a straight or circular 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 leading strong-coupling contributions to 4-point correlators of the simplest “protected” operators by starting with the AdS₅ × S⁵ string action expanded near the AdS₂ minimal surface and evaluating the corresponding tree-level AdS₂ Witten diagrams. Here 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” CFT₁ should have 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 S⁵ embedding coordinates and AdS₅ coordinates transverse to the minimal surface ending on the line at the boundary. The SO(6) symmetry is preserved on the string side provided the 5-sphere coordinates satisfy Neumann boundary conditions (as opposed to Dirichlet in the supersymmetric case); this implies that one should integrate over the S⁵ expansion point. The massless S⁵ fluctuations then 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 appearing in the 4-point functions turn out to have a more complicated structure than in the supersymmetric case, involving polylog (Li₃ and Li₂) functions. 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.