Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS${}_7\times$S${}^4$

Abstract

Surface operators in the 6d (2,0) theory at large $N$ have a holographic description in terms of M2 branes probing the AdS${}_7\times S^4$ M-theory background. The most symmetric, 1/2-BPS, operator is defined over a planar or spherical surface, and it preserves a 2d superconformal group. This includes, in particular, an $SO(2,2)$ subgroup of 2d conformal transformations, so that the surface operator may be viewed as a conformal defect in the 6d theory. The dual M2 brane has an AdS${}_3$ induced geometry, reflecting the 2d conformal symmetry. Here we use the holographic description to extract the defect CFT data associated to the surface operator. The spectrum of transverse fluctuations of the M2 brane is found to be in one-to-one correspondence with a protected multiplet of operator insertions on the surface, which includes the displacement operator. We compute the one-loop determinants of fluctuations of the M2 brane, and extract the conformal anomaly coefficient of the spherical surface to order $N^0$. We also briefly discuss the RG flow from the non-supersymmetric to the 1/2-BPS defect operator, and its consistency with a "$b$-theorem" for the defect CFT. Starting with the M2 brane action, we then use AdS${}_3$ Witten diagrams to compute the 4-point functions of the elementary bosonic insertions on the surface operator, and extract some of the defect CFT data from the OPE. The 4-point function is shown to satisfy superconformal Ward identities, and we discuss a related subsector of "twisted" scalar insertions, whose correlation functions are constrained by the residual superconformal symmetry.

29 pages, no figure; v2,v3: minor corrections and references added

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• Surface Defect, Anomalies and $b$-Extremization
• Broken global symmetries and defect conformal manifolds
• All Holographic Four-Point Functions in All Maximally Supersymmetric CFTs
• Wilson loops at large $N$ and the quantum M2 brane
• Conformal dispersion relations for defects and boundaries
• Defect CFT techniques in the 6d $\mathcal{N}=(2,0)$ theory
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Five-Dimensional Non-Lorentzian Conformal Field Theories and their Relation to Six-Dimensions
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• Coset space actions for nonrelativistic strings
• Observations on BPS observables in 6d
• RG Flows and Stability in Defect Field Theories
• Vortex loop operators and quantum M2-branes
• Ironing out the crease
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry
• Holographic M5 branes in $Ad{S}_7\times S^4$
• BPS surface operators and calibrations
• Rényi Entropy with Surface Defects in Six Dimensions
• Surface Operators in Superspace
• Holographic M-Brane Super-Embeddings
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories
• M5-brane prongs, string soliton bound states and wall-crossing
• On world-volume supersymmetry of supermembrane action in static gauge
• Universal sectors in superconformal defects
• $\kappa$-symmetric M5 brane web for defects in $Ad{S}_7/CF{T}_6$ holography