One-loop one-point functions in gauge-gravity dualities with defects

We initiate the calculation of loop corrections to correlation functions in 4D defect CFTs. More precisely, we consider N=4 SYM with a codimension-one defect separating two regions of space, x_3>0 and x_30. The holographic dual is the D3-D5 probe brane system where the D5 brane geometry is AdS_4...

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Bibliographic Details
Published in:arXiv.org 2016-12
Main Authors: Buhl-Mortensen, Isak, de Leeuw, Marius, Ipsen, Asger C, Kristjansen, Charlotte, Wilhelm, Matthias
Format: Article
Language:English
Subjects:
Defects
Dependence
Feynman diagrams
Mass matrix
Mathematical analysis
Minkowski space
Operators (mathematics)
Online Access:Get full text
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Summary:We initiate the calculation of loop corrections to correlation functions in 4D defect CFTs. More precisely, we consider N=4 SYM with a codimension-one defect separating two regions of space, x_3>0 and x_30. The holographic dual is the D3-D5 probe brane system where the D5 brane geometry is AdS_4 x S^2 and a background gauge field has k units of flux through the S^2. We diagonalise the mass matrix of the defect CFT making use of fuzzy-sphere coordinates and we handle the x_3-dependence of the mass terms in the 4D Minkowski space propagators by reformulating these as standard massive AdS_4 propagators. Furthermore, we show that only two Feynman diagrams contribute to the one-loop correction to the one-point function of any single-trace operator and we explicitly calculate this correction in the planar limit for the simplest chiral primary. The result of this calculation is compared to an earlier string-theory computation in a certain double-scaling limit, finding perfect agreement. Finally, we discuss how to generalise our calculation to any single-trace operator, to finite N and to other types of observables such as Wilson loops.
ISSN:2331-8422
DOI:10.48550/arxiv.1606.01886