Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop

TL;DR

This paper computes the structure constants of defect changing operators on the 1/2 BPS Wilson loop in planar N=4 super Yang-Mills, using perturbation theory and integrability techniques, providing exact results in a special limit.

Contribution

It introduces a novel calculation of structure constants at all orders in a specific limit, combining perturbative and integrability methods for defect CFTs.

Findings

Two-loop computations of three-point functions

Resummation of diagrams in the ladders limit

Exact structure constants at all orders in the rescaled coupling

Abstract

We study three-point functions of operators on the $1/2$ BPS Wilson loop in planar $\mathcal{N}=4$ super Yang-Mills theory. The operators we consider are "defect changing operators", which change the scalar coupled to the Wilson loop. We first perform the computation at two loops in general set-ups, and then study a special scaling limit called the ladders limit, in which the spectrum is known to be described by a quantum mechanics with the SL(2,$\mathbb{R}$) symmetry. In this limit, we resum the Feynman diagrams using the Schwinger-Dyson equation and determine the structure constants at all order in the rescaled coupling constant. Besides providing an interesting solvable example of defect conformal field theories, our result gives invaluable data for the integrability-based approach to the structure constants.