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<p>We study properties of point-like impurities preserving flavor symmetry and supersymmetry in four-dimensional 𝒩 = 2 field theories. At large distances, such impurities are described by half-BPS superconformal line defects. By working in the AdS<sub>2</sub> × S<sup>2</sup> 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 AdS<sub>2</sub> × S<sup>2</sup> conformal frame. We provide several consistency checks on our Ward identities.</p>

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Global symmetry and integral constraint on superconformal lines in four dimensions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月17日

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  • Ross Dempsey,
  • Bendeguz Offertaler,
  • Silviu S. Pufu,
  • Yifan Wang

摘要

We study properties of point-like impurities preserving flavor symmetry and supersymmetry in four-dimensional 𝒩 = 2 field theories. At large distances, such impurities are described by half-BPS superconformal line defects. By working in the AdS2 × S2 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 AdS2 × S2 conformal frame. We provide several consistency checks on our Ward identities.