Surprises in the Ordinary: $O(N)$ Invariant Surface Defect in the $\epsilon$-expansion

Oleksandr Diatlyk; Zimo Sun; Yifan Wang

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arXiv · 2411.16522

Surprises in the Ordinary: $O(N)$ Invariant Surface Defect in the $\epsilon$-expansion

Oleksandr Diatlyk·Zimo Sun·Yifan Wang

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Abstract

We study an $O(N)$ invariant surface defect in the Wilson-Fisher conformal field theory (CFT) in $d=4-\epsilon$ 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 $\epsilon$-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 $\epsilon$-expansion. We also analyze the full conformal anomalies for the surface defect.

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Oleksandr Diatlyk, Zimo Sun, Yifan Wang. 2024-11-25. Surprises in the Ordinary: $O(N)$ Invariant Surface Defect in the $\epsilon$-expansion. https://arxiv.org/abs/2411.16522

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