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.

arXiv comment29 pages, no figure; v2,v3: minor corrections and references added

References in corpus (78)

• Wilson loops in large N field theories
• The Holographic Weyl anomaly
• Heat kernel expansion: user's manual
• Correlation functions in the CFT(d)/AdS(d+1) correpondence
• Holography from Conformal Field Theory
• Open P-Branes
• Writing CFT correlation functions as AdS scattering amplitudes
• The Operator Product Expansion for Wilson Loops and Surfaces in the Large N Limit
• Comments on gluon scattering amplitudes via AdS/CFT
• Entropy of Near-Extremal Black p-branes
• Conformal Anomaly Of Submanifold Observables In AdS/CFT Correspondence
• Green-Schwarz String in AdS_5 x S^5: Semiclassical Partition Function
• An exact formula for the radiation of a moving quark in N=4 super Yang Mills
• Mellin amplitudes for $Ad{S}_5\times S^5$
• Anomaly polynomial of general 6d SCFTs
• Exact results for the entanglement entropy and the energy radiated by a quark
• How to Succeed at Holographic Correlators Without Really Trying
• W Symmetry in six dimensions
• Theta-terms in nonlinear sigma-models
• Entanglement Entropy, Trace Anomalies and Holography
• Superconformal Ward Identities and their Solution
• One Loop Tests of Higher Spin AdS/CFT
• Partial non-renormalisation of the stress-tensor four-point function in N=4 SYM and AdS/CFT
• Half-BPS Wilson loop and AdS${}_2$/CFT${}_1$
• R^4 terms in 11 dimensions and conformal anomaly of (2,0) theory
• A Constraint on Defect and Boundary Renormalization Group Flows
• Generalized quark-antiquark potential at weak and strong coupling
• All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry
• Defects in conformal field theory
• Anomaly Matching and a Hopf-Wess-Zumino Term in 6d, N=(2,0) Field Theories
• Correlation Functions and Massive Kaluza-Klein Modes in the AdS/CFT Correspondence
• Four-point Functions of Lowest Weight CPOs in N=4 SYM_4 in Supergravity Approximation
• Intersecting D3-branes and Holography
• Partition functions and double-trace deformations in AdS/CFT
• Bootstrapping the half-BPS line defect
• 1/2-BPS states in M theory and defects in the dual CFTs
• No-force condition and BPS combinations of p-branes in 11 and 10 dimensions
• Rényi entropy and conformal defects
• On Four-Point Functions of Half-BPS Operators in General Dimensions
• Towards a $C$-theorem in defect CFT
• Probing N=4 SYM With Surface Operators
• AdS Description of Induced Higher-Spin Gauge Theory
• Stringy Corrections to the Wilson Loop in N=4 Super Yang-Mills Theory
• The M-Theory Two-Brane in AdS_4 x S^7 and AdS_7 x S^4
• Partition function of free conformal higher spin theory
• Six-Dimensional Tensionless Strings In The Large N Limit
• $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3$ Tree-Level Correlators: Hidden Six-Dimensional Conformal Symmetry
• From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects
• Superprotected n-point correlation functions of local operators in N=4 super Yang-Mills
• The 1/N correction in the D3-brane description of circular Wilson loop at strong coupling
• On Superconformal Four-Point Mellin Amplitudes in Dimension $d>2$
• Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT
• Line defects and radiation in $\mathcal{N}=2$ theories
• Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT
• Exact Half-BPS Flux Solutions in M-theory II: Global solutions asymptotic to AdS_7 x S^4
• More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
• Recursion Relations in Witten Diagrams and Conformal Partial Waves
• Holographic Four-Point Functions in the (2, 0) Theory
• The Wilson loop CFT: Insertion dimensions and structure constants from wavy lines
• Superconformal surfaces in four dimensions
• Wilson Loop Renormalization Group Flows
• M5-branes and Wilson Surfaces
• Irreversibility in quantum field theories with boundaries
• Correlators on non-supersymmetric Wilson line in N=4 SYM and AdS${}_2$/CFT${}_1$
• Central Charges of 2d Superconformal Defects
• Excited States of One-Dimensional Defect CFTs from the Quantum Spectral Curve
• Conformal anomaly c-coefficients of superconformal 6d theories
• Holographic entanglement entropy from probe M-theory branes
• Bootstrapping line defects in $\mathcal{N}=2$ theories
• M5-branes and Wilson Surfaces in AdS${}_7$/CFT${}_6$ Correspondence
• Wilson Surface Central Charge from Holographic Entanglement Entropy
• Conformal anomaly of Wilson surface observables - a field theoretical computation
• Magnetic Interactions of D-branes and Wess-Zumino Terms in Super Yang-Mills Effective Actions
• AdS_3 OM theory and the self-dual string or Membranes ending on the Five-brane
• Chern-Simons theory from M5-branes and calibrated M2-branes
• Order $1/{\mathbf{N}}^3$ corrections to the conformal anomaly of the (2,0) theory in six dimensions
• Membrany corrections to the string anti-string potential in M5-brane theory
• Dynamics of a wavy plane Wilson surface observable from AdS-CFT correspondence

Cited by in corpus (29)

• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Bootstrapping the half-BPS line defect CFT in $\mathcal{N}=4$ SYM at strong coupling
• Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT${}_1$
• 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