Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM

TL;DR

This paper computes the two-point correlator of a specific operator in N=4 SYM with a Wilson line defect, deriving defect CFT data and confirming known anomalous dimensions and one-point functions.

Contribution

It provides a closed-form formula for defect CFT data in the presence of a Wilson line in N=4 SYM, combining perturbation theory and defect CFT techniques.

Findings

Derived defect CFT data and Taylor series expansion for the correlator.

Recovered anomalous dimensions of twist-two operators including the Konishi multiplet.

Validated one-point function of the stress-tensor multiplet against matrix-model results.

Abstract

We study the two-point function of the stress-tensor multiplet of $\mathcal{N}=4$ SYM in the presence of a line defect. To be more precise, we focus on the single-trace operator of conformal dimension two that sits in the $20'$ irrep of the $\mathfrak{so}(6)_\text{R}$ R-symmetry, and add a Maldacena-Wilson line to the configuration which makes the two-point function non-trivial. We use a combination of perturbation theory and defect CFT techniques to obtain results up to next-to-leading order in the coupling constant. Being a defect CFT correlator, there exist two (super)conformal block expansions which capture defect and bulk data respectively. We present a closed-form formula for the defect CFT data, which allows to write an efficient Taylor series for the correlator in the limit when one of the operators is close to the line. The bulk channel is technically harder and closed-form formulae are particularly challenging to obtain, nevertheless we use our analysis to check against well-known data of $\mathcal{N}=4$ SYM. In particular, we recover the correct anomalous dimensions of a famous tower of twist-two operators (which includes the Konishi multiplet), and successfully compare the one-point function of the stress-tensor multiplet with results obtained using matrix-model techniques.