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) 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) 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 ϵ-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 super-symmetric boundary using Feynman diagrams, and find perfect agreement between the perturbative and bootstrap results.
Highlights
Conformal field theories with boundaries have a wide variety of applications that range from condensed matter to string theory
We study a host of correlators using superspace techniques and calculate superconformal blocks for two- and three-point functions
They contain non-trivial dynamics akin to four-point functions in homogeneous CFTs, which is captured by the existence of two inequivalent conformal block expansions
Summary
Conformal field theories with boundaries have a wide variety of applications that range from condensed matter to string theory. In the presence of a boundary two-point correlators are not fixed by symmetry, but depend on a conformal invariant. They contain non-trivial dynamics akin to four-point functions in homogeneous CFTs, which is captured by the existence of two. One possibility is to fuse the two local operators together and calculate the resulting one-point functions in the presence of the boundary. There is a unique half-BPS boundary in 4d N = 1 which is non-chiral, and that can be interpolated to the N = (1, 1) boundary in 3d This is the BCFT counterpart of the results obtained in [24], where the bulk superconformal blocks were continued in d.
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