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

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## Abstract

This paper focuses on the analysis of 4*d* \( \mathcal{N} \) = 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 4*d* \( \mathcal{N} \) = 4 superconformal theories with a boundary, but also to three more systems that have the same symmetry algebra: 4*d* \( \mathcal{N} \) = 4 superconformal theories with a line defect, 3*d* \( \mathcal{N} \) = 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**

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