The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories

Abstract

6d (2,0) SCFTs of type $\mathfrak{g}$ have protected subsectors that were conjectured in arxiv:1404.1079 to be captured by ${\mathcal{W}}_{\mathfrak{g}}$ algebras. We write down the crossing equations for mixed four-point functions $⟨S_{k_1}{S}_{k_2}{S}_{k_3}{S}_{k_4}⟩$ of 1/2-BPS operators $S_{k_i}$ in 6d (2,0) theories and detail how a certain twist reduces this system to a 2d meromorphic CFT multi-correlator bootstrap problem. We identify the relevant 6d (2,0) $\mathcal{W}$-algebras of type $\mathfrak{g}=\{A_{N-1},D_N\}$ as truncations of ${\mathcal{W}}_{1+\infty }$ and solve OPE associativity conditions for their structure constants, both using $\text{OPEdefs}$ and the holomorphic bootstrap of arxiv:1503.07111. With this, we solve the multi-correlator bootstrap for twisted 6d four-point correlators ${\mathcal{F}}_{k_1{k}_2{k}_3{k}_4}$ involving all $S_{k_i}$ up to $\{k_i\}=4$ and extract closed-form expressions for 6d OPE coefficients. We describe the implications of our CFT data on conformal Regge trajectories of the (2,0) theories and finally, demonstrate the consistency of our results with protected higher-derivative corrections to graviton scattering in M-theory on $Ad{S}_7\times S^4/{\mathbb{Z}}_{\mathfrak{o}}$.

55 pages, 1 Mathematica notebook. v1: Comments are welcome. v2: References added and submitted for publication. v3: Added clarifications of 6d data extraction and the filtration ambiguity, and more references. v4: Matches published version. v5: Another clarification

References in corpus (98)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N=2 dualities
• Holography from Conformal Field Theory
• Conformal Four Point Functions and the Operator Product Expansion
• Baryons And Branes In Anti de Sitter Space
• Infinite Chiral Symmetry in Four Dimensions
• Open P-Branes
• Writing CFT correlation functions as AdS scattering amplitudes
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Analyticity in Spin in Conformal Theories
• Minimal Model Holography
• The N=4 Superconformal Bootstrap
• Bootstrapping Conformal Field Theories with the Extremal Functional Method
• Superconformal Symmetry, Correlation Functions and the Operator Product Expansion
• The $(2,0)$ superconformal bootstrap
• Triality in Minimal Model Holography
• Asymptotic W-symmetries in three-dimensional higher-spin gauge theories
• Conformal Partial Waves: Further Mathematical Results
• How to Succeed at Holographic Correlators Without Really Trying
• Analyticity and the Holographic S-Matrix
• W Symmetry in six dimensions
• Bounds in 4D Conformal Field Theories with Global Symmetry
• Superconformal Ward Identities and their Solution
• Vertex operator algebras, Higgs branches, and modular differential equations
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Holography in the Flat Space Limit
• R^4 terms in 11 dimensions and conformal anomaly of (2,0) theory
• Flat-space scattering and bulk locality in the AdS/CFT correspondence
• Anomaly Matching and a Hopf-Wess-Zumino Term in 6d, N=(2,0) Field Theories
• S-Matrices from AdS Spacetime
• The Large N 't Hooft Limit of Coset Minimal Models
• On Four-Point Functions of Half-BPS Operators in General Dimensions
• M Theory on AdS_p x S^{11-p} and Superconformal Field Theories
• More $\mathcal{N}=4$ superconformal bootstrap
• Solving M-theory with the Conformal Bootstrap
• The M-Theory S-Matrix From ABJM: Beyond 11D Supergravity
• VOAs labelled by complex reflection groups and 4d SCFTs
• Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT
• Integrability and Conformal Bootstrap: One Dimensional Defect CFT
• Correlation Functions of Operators and Wilson Surfaces in the d=6, (0,2) Theory in the Large N Limit
• Constraining conformal field theories with a higher spin symmetry
• Holographic Four-Point Functions in the (2, 0) Theory
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• The M-theory Archipelago
• All Tree-Level Correlators for M-theory on $Ad{S}_7\times S^4$
• Generalized bootstrap equations for N=4 SCFT
• M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture
• Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS${}_7\times$S${}^4$
• Macdonald Index and Chiral Algebra
• Exploring ${\mathcal{W}}_{\infty }$ in the quadratic basis
• Aspects of Superconformal Multiplets in D>4
• Even spin minimal model holography
• Bootstrapping the 3d Ising Stress Tensor
• Free Field Realizations from the Higgs Branch
• Three Point Functions of Chiral Primary Operators in d=3, N= 8 and d=6, N=(2,0) SCFT at Large N
• Universal properties of superconformal OPEs for 1/2 BPS operators in $3\le D\le 6$
• Solving Conformal Field Theories with Artificial Intelligence
• All Holographic Four-Point Functions in All Maximally Supersymmetric CFTs
• ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion
• Aspects of superconformal field theories in six dimensions
• 6d (2,0) and M-theory at 1-loop
• VOAs and rank-two instanton SCFTs
• Toda Theory From Six Dimensions
• Universal two-parameter ${\mathcal{W}}_{\infty }$-algebra and vertex algebras of type $\mathcal{W}(2,3,\dots ,N)$
• Schur sector of Argyres-Douglas theory and $W$-algebra
• An Algorithmic Approach to Operator Product Expansions, $W$-Algebras and $W$-Strings
• Universal two-parameter even spin ${\mathcal{W}}_{\infty }$-algebra
• M-theory Beyond The Supergravity Approximation
• Defect CFT techniques in the 6d $\mathcal{N}=(2,0)$ theory
• 6D (2,0) Bootstrap with soft-Actor-Critic
• More on holographic correlators: Twisted and dimensionally reduced structures
• Twisted Holography
• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• Regge trajectories for the (2,0) theories
• Recursion Relations for Anomalous Dimensions in the 6d $(2,0)$ Theory
• Bootstrapping mixed correlators in $\mathcal{N}=4$ Super Yang-Mills
• Pure anti-de Sitter supergravity and the conformal bootstrap
• Higher-spin gauge theories in three spacetime dimensions
• Order $1/{\mathbf{N}}^3$ corrections to the conformal anomaly of the (2,0) theory in six dimensions
• Renyi Entropies, the Analytic Bootstrap, and 3D Quantum Gravity at Higher Genus
• Comments on chiral algebras and $\Omega$-deformations
• On even spin $W_{\infty }$
• Conformal Bootstrap with Reinforcement Learning
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Bootstrability in Line-Defect CFT with Improved Truncation Methods
• Scattering States in AdS/CFT
• Free field realizations for rank-one SCFTs
• 6d Large Charge and 2d Virasoro Blocks
• Higher-derivative corrections in M-theory from precision numerical bootstrap
• Composite operators in $\mathcal{N}=4$ Super Yang-Mills
• Dissecting supergraviton six-point function with lightcone limits and chiral algebra
• Extremal couplings, graviton exchange, and gluon scattering in AdS
• Conformal dispersion relation for mixed correlators
• Structure of the $\mathcal{N}=4$ chiral algebra
• A universal W-algebra for N=4 super Yang-Mills
• Vertex algebra of extended operators in 4d N=2 superconformal field theories
• Bootstrapping M-theory Orbifolds

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