Abstract
We study correlation functions of local operator insertions on the 1/2-BPS Wilson line in N=4 super Yang–Mills theory. These correlation functions are constrained by the 1d superconformal symmetry preserved by the 1/2-BPS Wilson line and define a defect CFT1 living on the line. At strong coupling, a set of elementary operator insertions with protected scaling dimensions correspond to fluctuations of the dual fundamental string in AdS×5S5 ending on the line at the boundary and can be thought of as light fields propagating on the AdS2 worldsheet. We use AdS/CFT techniques to compute the tree-level AdS2 Witten diagrams describing the strong coupling limit of the four-point functions of the dual operator insertions. Using the OPE, we also extract the leading strong coupling corrections to the anomalous dimensions of the “two-particle” operators built out of elementary excitations. In the case of the circular Wilson loop, we match our results for the 4-point functions of a special type of scalar insertions to the prediction of localization to 2d Yang–Mills theory.
Highlights
We study correlation functions of local operator insertions on the 1/2-BPS Wilson line in N = 4 super Yang-Mills theory
One should normalize the correlator on the right-hand side by the expectation value of the Wilson loop without insertions
Among the possible operator insertions, a special role is played by a set of “elementary excitations” that fall into a short representation of the OSp(4∗|4) symmetry with 8 bosonic plus 8 fermionic operators, and have protected scaling dimensions
Summary
Before proceeding to computation of correlators of 2d fields in the AdS2 theory (2.4),(2.5) let us make some general remarks about the structure of four-point functions in CFT1. Local operators in a d = 1 CFT defined on a line R = {t} which are covariant under the conformal group SO(2, 1) are labelled just by their scaling dimension ∆ (and possibly by some representation of an internal symmetry group which we suppress ). Let us consider the 4-point function of an operator O∆(t). The SO(2, 1) symmetry restricts the 4-point function to take the form. We will need the case of correlator of operators with pairwise equal dimensions. One may write the 4-point function in the form.
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