Superconformal Boundaries in $4-\epsilon$ dimensions

Abstract

Boundaries in three-dimensional $\mathcal{N}=2$ superconformal theories may preserve one half of the original bulk supersymmetry. There are two possibilities which are characterized by the chirality of the leftover supercharges. Depending on the choice, the remaining $2d$ boundary algebra exhibits $\mathcal{N}=(0,2)$ or $\mathcal{N}=(1,1)$ supersymmetry. In this work we focus on correlation functions of chiral fields for both types of supersymmetric boundaries. We study a host of correlators using superspace techniques and calculate superconformal blocks for two- and three-point functions. For $\mathcal{N}=(1,1)$ supersymmetry, some of our results can be analytically continued in the spacetime dimension while keeping the codimension fixed. This opens the door for a bootstrap analysis of the $\epsilon$-expansion in supersymmetric BCFTs. Armed with our analytically-continued superblocks, we prove that in the free theory limit two-point functions of chiral (and antichiral) fields are unique. The first order correction, which already describes interactions, is universal up to two free parameters. As a check of our analysis, we study the Wess-Zumino model with a supersymmetric boundary using Feynman diagrams, and find perfect agreement between the perturbative and bootstrap results.

arXiv comment45 pages, no figures

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• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap
• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• On Analytic Bootstrap for Interface and Boundary CFT
• A dispersion relation for defect CFT
• Fermions in Boundary Conformal Field Theory : Crossing Symmetry and $\epsilon$-Expansion
• Bootstrapping Monodromy Defects in the Wess-Zumino Model
• Conformal dispersion relations for defects and boundaries
• Conformal Bootstrap near the edge
• Defect Conformal Blocks from Appell Functions
• Universal Spinning Casimir Equations and Their Solutions
• The ordinary surface universality class of the three-dimensional O($N$) model
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators