Marginal deformations and defect anomalies

摘要: We deform a defect conformal field theory by an exactly marginal bulk operator and we consider the dependence on coupling of flat spherical expectation values. For even dimensional defects find logarithmic divergence which can be related to $a$-type anomaly coefficient. This coefficient, for theories, is not invariant manifold its controlled all orders one-point function associated operator. odd-dimensional defects, case exhibit different qualitative behaviors, generalizing arbitrary dimensions line-circle superconformal Wilson loops. Our results also imply non-trivial recently proposed $C$-function. finally apply our general result few specific examples, including loops Renyi entropy.