Bootstrapping the half-BPS line defect

TL;DR

This paper applies bootstrap techniques to study half-BPS line defects in 4d N=4 superconformal theories, providing bounds on operator data and suggesting a unique solution consistent with known Wilson line behavior.

Contribution

It introduces a bootstrap analysis of 1d superconformal defects, including numerical bounds and a potential unique solution aligned with strong coupling limits.

Findings

Numerical bounds on OPE coefficients and conformal dimensions.

Identification of a numerical island indicating a unique crossing solution.

Perturbative analysis near strong coupling matches numerical bounds.

Abstract

We use modern bootstrap techniques to study half-BPS line defects in 4d N=4 superconformal theories. Specifically, we consider the 1d CFT with OSP(4*|4) superconformal symmetry living on such a defect. Our analysis is general and based only on symmetries, it includes however important examples like Wilson and 't Hooft lines in N=4 super Yang-Mills. We present several numerical bounds on OPE coefficients and conformal dimensions. Of particular interest is a numerical island obtained from a mixed correlator bootstrap that seems to imply a unique solution to crossing. The island is obtained if some assumptions about the spectrum are made, and is consistent with Wilson lines in planar N=4 super Yang-Mills at strong coupling. We further analyze the vicinity of the strong-coupling point by calculating perturbative corrections using analytic methods. This perturbative solution has the sparsest spectrum and is expected to saturate the numerical bounds, explaining some of the features of our numerical results.