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

Abstract

Abstract 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.

Keywords

• Renormalization Group
• Scale and Conformal Symmetries