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Abstract We study co-dimension two monodromy defects in theories of conformally coupled scalars and free Dirac fermions in arbitrary d dimensions. We characterise this family of conformal defects by computing the one-point functions of the stress-tensor and conserved current for Abelian flavour symmetries as well as two-point functions of the displacement operator. In the case of d = 4, the normalisation of these correlation functions are related to defect Weyl anomaly coefficients, and thus provide crucial information about the defect conformal field theory. We provide explicit checks on the values of the defect central charges by calculating the universal part of the defect contribution to entanglement entropy, and further, we use our results to extract the universal part of the vacuum Rényi entropy. Moreover, we leverage the non-supersymmetric free field results to compute a novel defect Weyl anomaly coefficient in a d = 4 theory of free N $$ \mathcal{N} $$ = 2 hypermultiplets. Including singular modes in the defect operator product expansion of fundamental fields, we identify notable relevant deformations in the singular defect theories and show that they trigger a renormalisation group flow towards an IR fixed point with the most regular defect OPE. We also study Gukov-Witten defects in free d = 4 Maxwell theory and show that their central charges vanish.

Abstract We use renormalization group methods to study composite operators existing at a boundary of an interacting conformal field theory. In particular we relate the data on boundary operators to short-distance (near-boundary) divergences of bulk two-point functions. We further argue that in the presence of running couplings at the boundary the anomalous dimensions of certain composite operators can be computed from the relevant beta functions and remark on the implications for the boundary (pseudo) stress-energy tensor. We apply the formalism to a scalar field theory in d = 3−𝜖 dimensions with a quartic coupling at the boundary whose beta function we determine to the first non-trivial order. We study the operators in this theory and compute their conformal data using 𝜖 −expansion at the Wilson-Fisher fixed point of the boundary renormalization group flow. We find that the model possesses a non-zero boundary stress-energy tensor and displacement operator both with vanishing anomalous dimensions. The boundary stress tensor decouples at the fixed point in accordance with Cardy’s condition for conformal invariance. We end the main part of the paper by discussing the possible physical significance of this fixed point for various values of 𝜖.

Abstract We study the momentum space representation of energy-momentum tensor two-point functions on a space with a planar boundary in d = 3. We show that non-conservation of momentum in the direction perpendicular to the boundary allows for new phenomena compared to the boundary-less case. Namely we demonstrate how local contact terms arise when the correlators are expanded in the regime where parallel momentum is small compared to the perpendicular one, which corresponds to the near-boundary limit. By exploring two-derivative counterterms involving components of Riemann tensor we identify a finite, scheme-independent part of the two-point function. We then relate this component to the conformal anomaly c ∂ proportional to the boundary curvature R ^ $$ \widehat{R} $$ . In the formalism of this paper c ∂ arises due to integrating out bulk modes coupled to the curved space, which generate local contributions the effective action at the boundary. To calculate the anomaly in specific (free-field) examples, we combine the method of images with Feynman diagrammatic techniques and propose a general methodology for perturbative computations of this type. The framework is tested by computing c ∂ on the explicit example of free scalar with mixed boundary conditions where we find agreement with the literature.