Multipoint correlators on the supersymmetric Wilson line defect CFT II: Unprotected operators

TL;DR

This paper develops a recursive method to compute multipoint scalar correlators on the supersymmetric Wilson line defect in N=4 SYM at weak coupling, including unprotected operators, and verifies the results with conformal block analysis.

Contribution

It introduces a weak-coupling recursion relation for next-to-leading order correlators involving unprotected scalars on the defect CFT, enabling explicit multi-point calculations.

Findings

Explicit six-point correlator results provided.

Conformal block expansion confirms consistency of low-lying CFT data.

Method extends to composite operators by scalar pinching.

Abstract

We continue our study of multipoint correlators of scalar fields on the $1d$ defect CFT generated by inserting operators along the Maldacena-Wilson line in $\mathcal{N} = 4$ SYM. We present a weak-coupling recursion relation that captures correlators at next-to-leading order involving an arbitrary number of the elementary scalar fields $\phi^i$ and $\phi^6$, the latter being unprotected. We can then build correlators of composite operators by pinching the scalar fields together. As a demonstration of our method, we give explicit results for correlators containing up to six points. We also expand some selected correlators using recently obtained conformal blocks in the comb and snowflake channel, and check that the extracted low-lying CFT data is consistent with explicit computations.