A Quantum Check of AdS/dCFT

Abstract

We build the framework for performing loop computations in the defect version of N=4 super Yang-Mills theory which is dual to the probe D5-D3 brane system with background gauge-field flux. In this dCFT, a codimension-one defect separates two regions of space-time with different ranks of the gauge group and three of the scalar fields acquire non-vanishing and space-time-dependent vacuum expectation values. The latter leads to a highly non-trivial mass mixing problem between different colour and flavour components, which we solve using fuzzy-sphere coordinates. Furthermore, the resulting space-time dependence of the theory's Minkowski space propagators is handled by reformulating these as propagators in an effective AdS4. Subsequently, we initiate the computation of quantum corrections. The one-loop correction to the one-point function of any local gauge-invariant scalar operator is shown to receive contributions from only two Feynman diagrams. We regulate these diagrams using dimensional reduction, finding that one of the two diagrams vanishes, and discuss the procedure for calculating the one-point function of a generic operator from the SU(2) subsector. Finally, we explicitly evaluate the one-loop correction to the one-point function of the BPS vacuum state, finding perfect agreement with an earlier string-theory prediction. This constitutes a highly non-trivial test of the gauge-gravity duality in a situation where both supersymmetry and conformal symmetry are partially broken.

arXiv comment41 pages; v2: typos corrected, one comment added, matches published version

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Cited by in corpus (27)

• Scalar one-point functions and matrix product states of AdS/dCFT
• Asymptotic one-point functions in AdS/dCFT
• Spin Chain Overlaps and the Twisted Yangian
• 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
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• On Marginal Operators in Boundary Conformal Field Theory
• One-Point Functions of Non-protected Operators in the SO(5) symmetric D3-D7 dCFT
• One-point functions in AdS/dCFT
• Integrable domain walls in ABJM theory
• A Quantum Check of Non-Supersymmetric AdS/dCFT
• String integrability of defect CFT and dynamical reflection matrices
• Supersymmetric D3/D5 for massive defects on curved space
• Thermal expectation values of fermions on anti-de Sitter space-time
• 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 Quantum Framework for AdS/dCFT through Fuzzy Spherical Harmonics on $S^4$
• Quark-antiquark potential in defect conformal field theory
• Two-point functions of SU(2)-subsector and length-two operators in dCFT
• 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
• Line and surface defects in 5D N=2 SCFT from matter-coupled F(4) gauged supergravity
• One-point functions in $\beta$-deformed N = 4 SYM with defect
• Wilson loops correlators in defect $\mathcal{N}=4$ SYM
• Integrability and Conformal Blocks for Surface Defects in $\mathcal{N}=4$ SYM
• B-type anomaly coefficients for the D3-D7 domain wall