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Journal of High Energy Physics

, 2017:122 | Cite as

Bootstrap equations for \( \mathcal{N} \) = 4 SYM with defects

  • Pedro Liendo
  • Carlo Meneghelli
Open Access
Regular Article - Theoretical Physics

Abstract

This paper focuses on the analysis of 4d \( \mathcal{N} \) = 4 superconformal theories in the presence of a defect from the point of view of the conformal bootstrap. We will concentrate first on the case of codimension one, where the defect is a boundary that preserves half of the supersymmetry. After studying the constraints imposed by supersymmetry, we will obtain the Ward identities associated to two-point functions of \( \frac{1}{2} \) -BPS operators and write their solution as a superconformal block expansion. Due to a surprising connection between spacetime and R-symmetry conformal blocks, our results not only apply to 4d \( \mathcal{N} \) = 4 superconformal theories with a boundary, but also to three more systems that have the same symmetry algebra: 4d \( \mathcal{N} \) = 4 superconformal theories with a line defect, 3d \( \mathcal{N} \) = 4 superconformal theories with no defect, and OSP(4|4) superconformal quantum mechanics. The superconformal algebra implies that all these systems possess a closed subsector of operators in which the bootstrap equations become polynomial constraints on the CFT data. We derive these truncated equations and initiate the study of their solutions.

Keywords

Conformal Field Theory Superspaces 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.IMIP, Humboldt-Universität zu Berlin, IRIS AdlershofBerlinGermany
  2. 2.Simons Center for Geometry and PhysicsStony Brook UniversityStony BrookU.S.A.

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