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

Pedro Liendo (IMIP, Humboldt-Universität zu Berlin, IRIS Adlershof, Zum Großen Windkanal 6, 12489, Berlin, Germany) ; Carlo Meneghelli (Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY, 11794-3636, U.S.A.)

This paper focuses on the analysis of 4 d N $$ \mathcal{N} $$ = 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 1 2 $$ \frac{1}{2} $$ -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 N $$ \mathcal{N} $$ = 4 superconformal theories with a boundary, but also to three more systems that have the same symmetry algebra: 4 d N $$ \mathcal{N} $$ = 4 superconformal theories with a line defect, 3 d N $$ \mathcal{N} $$ = 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.

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      "source": "Springer/SISSA", 
      "value": "This paper focuses on the analysis of 4 d N $$ \\mathcal{N} $$ = 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 1 2 $$ \\frac{1}{2} $$ -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 N $$ \\mathcal{N} $$ = 4 superconformal theories with a boundary, but also to three more systems that have the same symmetry algebra: 4 d N $$ \\mathcal{N} $$ = 4 superconformal theories with a line defect, 3 d N $$ \\mathcal{N} $$ = 4 superconformal theories with no defect, and OSP(4 \u2217 |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."
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Published on:
27 January 2017
Publisher:
Springer/SISSA
Published in:
Journal of High Energy Physics (2017)

DOI:
https://doi.org/10.1007/JHEP01(2017)122
arXiv:
1608.05126
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: