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<p>We study an <i>O</i>(<i>N</i>) invariant surface defect in the Wilson-Fisher conformal field theory (CFT) in <i>d</i> = 4 – <i>ϵ</i> dimensions. This defect is defined by mass deformation on a two-dimensional surface that generates localized disorder and is conjectured to factorize into a pair of ordinary boundary conditions in <i>d</i> = 3. We determine defect CFT data associated with the lightest <i>O</i>(<i>N</i>) singlet and vector operators up to the third order in the <i>ϵ</i>-expansion, find agreements with results from numerical methods and provide support for the factorization proposal in <i>d</i> = 3. Along the way, we observe surprising non-renormalization properties for surface anomalous dimensions and operator-product-expansion coefficients in the <i>ϵ</i>-expansion. We also analyze the full conformal anomalies for the surface defect.</p>

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Surprises in the ordinary: O(N) invariant surface defect in the ϵ-expansion

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月13日

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  • Oleksandr Diatlyk,
  • Zimo Sun,
  • Yifan Wang

摘要

We study an O(N) invariant surface defect in the Wilson-Fisher conformal field theory (CFT) in d = 4 – ϵ dimensions. This defect is defined by mass deformation on a two-dimensional surface that generates localized disorder and is conjectured to factorize into a pair of ordinary boundary conditions in d = 3. We determine defect CFT data associated with the lightest O(N) singlet and vector operators up to the third order in the ϵ-expansion, find agreements with results from numerical methods and provide support for the factorization proposal in d = 3. Along the way, we observe surprising non-renormalization properties for surface anomalous dimensions and operator-product-expansion coefficients in the ϵ-expansion. We also analyze the full conformal anomalies for the surface defect.