Superconformal Boundaries in $4-\epsilon$ dimensions

TL;DR

This paper investigates superconformal boundaries in 3D $ =2$ theories, computes correlation functions and superconformal blocks, and applies bootstrap techniques to analyze boundary supersymmetry and interactions.

Contribution

It introduces superspace methods for boundary correlators, derives superconformal blocks, and extends results via analytic continuation for bootstrap analysis in supersymmetric BCFTs.

Findings

Two-point functions are unique in free theory limit.

First-order interaction corrections are universal with two free parameters.

Bootstrap results agree with perturbative calculations in the Wess-Zumino model.

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.