Global Symmetry and Integral Constraint on Superconformal Lines in Four Dimensions

TL;DR

This paper develops a new method to derive superconformal Ward identities for line defects in 4D ${ m N}=2$ theories, simplifying the analysis of flavor current correlators and establishing integral constraints.

Contribution

It introduces a novel approach using the $ ext{AdS}_2 imes ext{S}^2$ conformal frame to derive and simplify superconformal Ward identities for line defects in four-dimensional supersymmetric theories.

Findings

Derived superconformal Ward identities using a new conformal frame approach.

Simplified the computation of integrated two-point functions of flavor currents.

Established integral constraints on flavor current correlators in ${ m N}=2$ theories.

Abstract

We study properties of point-like impurities preserving flavor symmetry and supersymmetry in four-dimensional ${\cal N} = 2$ field theories. At large distances, such impurities are described by half-BPS superconformal line defects. By working in the $\text{AdS}_2\times \text{S}^2$ conformal frame, we develop a novel and simpler way of deriving the superconformal Ward identities relating the various two-point functions of flavor current multiplet operators in the presence of the defect. We use these relations to simplify a certain integrated two-point function of flavor current multiplet operators that, in Lagrangian theories, can be computed using supersymmetric localization. The simplification gives an integral constraint on the two-point function of the flavor current multiplet superconformal primary with trivial integration measure in the $\text{AdS}_2\times \text{S}^2$ conformal frame. We provide several consistency checks on our Ward identities.