How a-type anomalies can depend on marginal couplings

Abstract

Even dimensional defects and boundaries in conformal field theory support type $a$ anomalies on their world-volume. We show that the one-point functions of marginal operators, in the presence of defects and boundaries, are anomalous, and that the Wess-Zumino consistency condition relates them to the derivative of the $a$-anomaly with respect to the marginal coupling. We also argue that the constant term $F$ for odd dimensional surfaces can depend on marginal parameters.

arXiv comment5 pages. v2: references added, v3: grant info added

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• Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects
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• Deep Boundary Perturbations at a Quantum Critical Point