Universality at large transverse spin in defect CFT

TL;DR

This paper investigates the universal behavior of defect operators in conformal field theories at large transverse spin, revealing accumulation points and Regge trajectories using a bulk-to-defect OPE inversion formula, with implications for Wilson lines.

Contribution

It introduces a new inversion formula for the bulk-to-defect OPE, demonstrating universal spectral features at large transverse spin in defect CFTs, supported by perturbative and holographic examples.

Findings

Existence of universal accumulation points in defect operator spectrum at large s

Alignment of defect operator scaling dimensions in Regge trajectories

Predictions for defect spectra on Wilson lines

Abstract

We study the spectrum of local operators living on a defect in a generic conformal field theory, and their coupling to the local bulk operators. We establish the existence of universal accumulation points in the spectrum at large $s$, $s$ being the charge of the operators under rotations in the space transverse to the defect. Our tools include a formula that inverts the bulk to defect OPE, analogous to the Caron-Huot formula for the four-point function. Analyticity of the formula in $s$ implies that the scaling dimensions of the defect operators are aligned in Regge trajectories $\widehat{\Delta}(s)$. These results require the correlator of two local operators and the defect to be bounded in a certain region, a condition that we do not prove in general. We check our conclusions against examples in perturbation theory and holography, and we make specific predictions concerning the spectrum of defect operators on Wilson lines. We also give an interpretation of the large $s$ spectrum in the spirit of the work of Alday and Maldacena.