Integral Identities from Symmetry Breaking of Conformal Defects

Abstract

In conformal field theory, the insertion of a defect breaks part of the global symmetry and gives rise to defect operators such as the tilts and displacements. We establish identities relating the integrated four-point functions of such operators to their two-point functions, derived both from the geometric properties of the defect conformal manifold, which is the symmetry-breaking coset, and from the Lie algebra of the corresponding broken symmetry generators. As an explicit example, we demonstrate these integral identities in the case of the 1/2 BPS Maldacena-Wilson loop in $\mathcal{N} = 4$ SYM. This contribution serves as a brief review of the main ideas of Phys. Rev. Lett. 129, 201603 (2022), as well as a short preview of our forthcoming paper with Nadav Drukker and Petr Kravchuk. Here we present an independent derivation of the integral identities that will not appear in that work.