Nonlinearly Realised Defect Symmetries and Anomalies

TL;DR

The paper develops a framework to study nonlinear, finite deformations of conformal defects by mapping deformations to correlation functions of displacement and tilt operators, clarifying scheme-dependent versus independent data via a Wess-Zumino consistency structure. It derives universal integral identities for tilt and displacement correlators, uncovering anomaly terms for line and surface defects and identifying scheme-independent components that constrain defect CFT data beyond linear order. The work connects these identities to known results in supersymmetric theories and holographic contexts, and demonstrates how higher-point functions and cross-ratio data encode anomaly and OPE information. Overall, it provides a robust, general methodology for constraining defect operator algebras and their anomalies across a wide range of theories and defect types.

Abstract

Conformal defects -- extended objects in conformal field theories -- carry localised excitations inherited from symmetry currents, known as the displacements and tilts. They capture the linear response of the defect to deformations of its shape or of its profile along internal symmetry directions. There is no universal formula for deformations beyond the linear order and this is subject to ambiguities of coordinate choices on coset spaces and scheme dependence in the quantum theory. We analyse the exact match between the two and identify the scheme independent quantities capturing nonlinearly realised symmetries. This leads to universal integral identities for correlation functions in the presence of tilts and displacements. We present several applications of them. We also study possible anomalies, recovering known ones, finding new expressions for them, and uncovering new ones.