Broken global symmetries and defect conformal manifolds

Abstract

Just as exactly marginal operators allow to deform a conformal field theory along the space of theories known as the conformal manifold, appropriate operators on conformal defects allow for deformations of the defects. When a defect breaks a global symmetry, there is a contact term in the conservation equation with an exactly marginal defect operator. The resulting defect conformal manifold is the symmetry breaking coset and its Zamolodchikov metric is expressed as the 2-point function of the exactly marginal operator. As the Riemann tensor on the conformal manifold can be expressed as an integrated 4-point function of the marginal operators, we find an exact relation to the curvature of the coset space. We confirm this relation against previously obtained 4-point functions for insertions into the 1/2 BPS Wilson loop in $\mathcal{N}=4$ SYM and 3d $\mathcal{N}=6$ theory and the 1/2 BPS surface operator of the 6d $\mathcal{N}=(2,0)$ theory.

v1: 19 pages; v2: Scope of paper broadened a bit and title changed to reflect that. Added the case of ABJM and shortened to 7 pages (2-column). Version to appear in PRL

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Cited by in corpus (12)

• Line Defect RG Flows in the $\epsilon$ Expansion
• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
• 1/3 BPS loops and defect CFTs in ABJM theory
• RG Flows and Stability in Defect Field Theories
• The O(N)-flavoured replica twist defect
• Conformal line defects at finite temperature
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking
• Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories
• Fine Spectrum from Crude Analytic Bootstrap
• A network of hyperloops
• Universal sectors in superconformal defects