Marginal deformations and defect anomalies

Abstract

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

arXiv comment8 pages, v2: derivation on coupling independence for superconformal surface defects added

References in corpus (36)

• Wilson loops in large N field theories
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Wilson Loops in N=4 Supersymmetric Yang--Mills Theory
• An Exact Prediction of N=4 SUSYM Theory for String Theory
• A refinement of entanglement entropy and the number of degrees of freedom
• Conformal Anomaly Of Submanifold Observables In AdS/CFT Correspondence
• An exact formula for the radiation of a moving quark in N=4 super Yang Mills
• Exact results for the entanglement entropy and the energy radiated by a quark
• Exactly Marginal Deformations and Global Symmetries
• Deformations of Superconformal Theories
• A Constraint on Defect and Boundary Renormalization Group Flows
• Energy Momentum Tensor in Conformal Field Theories Near a Boundary
• Central Charges for BCFTs and Holography
• Defects in conformal field theory
• A General Proof of the Quantum Null Energy Condition
• Rényi entropy and conformal defects
• Towards a $C$-theorem in defect CFT
• Probing N=4 SYM With Surface Operators
• On Holographic Defect Entropy
• Exact results for static and radiative fields of a quark in N=4 super Yang-Mills
• The Exact Bremsstrahlung Function in N=2 Superconformal Field Theories
• Universality in the geometric dependence of Renyi entropy
• Wilson loop correlators at strong coupling: from matrices to bubbling geometries
• From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects
• Wilson Loops in N=2 Super-Yang-Mills from Matrix Model
• The generalized cusp in ABJ(M) N = 6 Super Chern-Simons theories
• Line defects and radiation in $\mathcal{N}=2$ theories
• Shape Dependence of Holographic Rényi Entropy in General Dimensions
• Holographic RG Flow on the Defect and g-Theorem
• Probing N=2 superconformal field theories with localization
• The 1/2 BPS Wilson loop in ABJ(M) at two loops: The details
• Perturbative evaluation of circular 1/2 BPS Wilson loops in N = 6 Super Chern-Simons theories
• BPS Wilson loops in $\mathcal{N}\ge 2$ superconformal Chern-Simons-matter theories
• Gravitational dual of the Rényi twist displacement operator

Cited by in corpus (12)

• Renormalization Group Flows on Line Defects
• Superconformal surfaces in four dimensions
• Surface Defect, Anomalies and $b$-Extremization
• Central Charges of 2d Superconformal Defects
• A Scaling Limit for Line and Surface Defects
• Monodromy Defects in Free Field Theories
• Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects
• Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• How a-type anomalies can depend on marginal couplings
• Boundary entropy under ambient RG flow in the AdS/BCFT model
• Anomalies from correlation functions in defect conformal field theory