Notes on a surface defect in the O(N) model

A bstract We study a surface defect in the free and critical O ( N ) vector models, defined by adding a quadratic perturbation localized on a two-dimensional subspace of the d -dimensional CFT. We compute the beta function for the corresponding defect renormalization group (RG) flow, and provide evidence that at long distances the system flows to a nontrivial defect conformal field theory (DCFT). We use epsilon and large N expansions to compute several physical quantities in the DCFT, finding agreement across different expansion methods. We also compute the defect free energy, and check consistency with the so-called b -theorem for RG flows on surface defects.