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

Abstract

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_3<0, where the gauge group is SU(N) and SU(N-k), respectively. This set-up is made possible by some of the real scalar fields acquiring a non-vanishing and x_3-dependent vacuum expectation value for x_3>0. 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.

7 pages, 3 figures, 1 table; v2: shortened, regularisation changed, match with string theory, v3: typo in table corrected, title changed to match journal version

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• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Spinning strings and AdS/CFT duality
• Four-Loop Cusp Anomalous Dimension From Obstructions
• AdS/dCFT one-point functions of the SU(3) sector
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Cited by in corpus (42)

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• Structure constants at wrapping order
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills
• Asymptotic one-point functions in AdS/dCFT
• Spin Chain Overlaps and the Twisted Yangian
• Boundary states, overlaps, nesting and bootstrapping AdS/dCFT
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Two-point functions in AdS/dCFT and the boundary conformal bootstrap equations
• A Quantum Check of AdS/dCFT
• One-Point Functions of Non-protected Operators in the SO(5) symmetric D3-D7 dCFT
• Boundary state bootstrap and asymptotic overlaps in AdS/dCFT
• One-point functions in AdS/dCFT
• Integrable domain walls in ABJM theory
• One-loop Wilson loops and the particle-interface potential in AdS/dCFT
• A Quantum Check of Non-Supersymmetric AdS/dCFT
• Overlaps for Matrix Product States of Arbitrary Bond Dimension in ABJM theory
• String integrability of defect CFT and dynamical reflection matrices
• Supersymmetric D3/D5 for massive defects on curved space
• Circular Wilson loops in defect Conformal Field Theory
• String integrability of the ABJM defect
• Volume complexity for the non-supersymmetric Janus AdS${}_5$ geometry
• A non-integrable quench from AdS/dCFT
• A Quantum Framework for AdS/dCFT through Fuzzy Spherical Harmonics on $S^4$
• ABJM quantum spectral curve and Mellin transform
• Quark-antiquark potential in defect conformal field theory
• Two-point functions of SU(2)-subsector and length-two operators in dCFT
• Introduction to Integrability and One-point Functions in $\mathcal{N}=4$ SYM and its Defect Cousin
• On actions for (entangling) surfaces and DCFTs
• Wrapping corrections for long range spin chains
• Holographic correlators of semiclassical states in defect CFTs
• Circular Wilson loops in defect $\mathcal{N}$=4 SYM: phase transitions, double-scaling limits and OPE expansion
• Lifting integrable models and long-range interactions
• B-type anomaly coefficients for the D3-D5 domain wall
• On analytical perturbative solution of ABJM quantum spectral curve
• The dilatation operator for defect conformal N=4 SYM
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• TCSA and the finite volume boundary state
• One-point functions in $\beta$-deformed N = 4 SYM with defect
• Wilson loops correlators in defect $\mathcal{N}=4$ SYM
• One-point functions for doubly-holographic BCFTs and backreacting defects
• Wilson lines in AdS/dCFT