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

Abstract

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 $$ \mathcal{N}=4 $$ 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 × S 5 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 S 5 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 S 5 expansion point. The massless S 5 fluctuations then have logarithmic propagator, corresponding to the boundary scalar operator having dimension $$ \Delta =\frac{5}{\sqrt{\lambda }}+\dots $$ Δ = 5 λ + … 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.