The $(2,0)$ superconformal bootstrap

Abstract

We develop the conformal bootstrap program for six-dimensional conformal field theories with $(2,0)$ supersymmetry, focusing on the universal four-point function of stress tensor multiplets. We review the solution of the superconformal Ward identities and describe the superconformal block decomposition of this correlator. We apply numerical bootstrap techniques to derive bounds on OPE coefficients and scaling dimensions from the constraints of crossing symmetry and unitarity. We also derive analytic results for the large spin spectrum using the lightcone expansion of the crossing equation. Our principal result is strong evidence that the $A_1$ theory realizes the minimal allowed central charge $(c=25)$ for any interacting $(2,0)$ theory. This implies that the full stress tensor four-point function of the $A_1$ theory is the unique unitary solution to the crossing symmetry equation at $c=25$. For this theory, we estimate the scaling dimensions of the lightest unprotected operators appearing in the stress tensor operator product expansion. We also find rigorous upper bounds for dimensions and OPE coefficients for a general interacting $(2,0)$ theory of central charge $c$. For large $c$, our bounds appear to be saturated by the holographic predictions obtained from eleven-dimensional supergravity.

58 pages (41 plus three appendices), 15 figures

References in corpus (34)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Bounds on 4D Conformal and Superconformal Field Theories
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
• Four-Dimensional SCFTs from M5-Branes
• M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills
• On D=5 super Yang-Mills theory and (2,0) theory
• Anomaly polynomial of general 6d SCFTs
• Bounds in 4D Conformal Field Theories with Global Symmetry
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Boundary and Interface CFTs from the Conformal Bootstrap
• Central Charge Bounds in 4D Conformal Field Theory
• Heisenberg Groups and Noncommutative Fluxes
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• Universal anomalous dimensions at large spin and large twist
• Bootstrapping the Three-Dimensional Supersymmetric Ising Model
• Five dimensional $O(N)$-symmetric CFTs from conformal bootstrap
• Bootstrapping SCFTs with Four Supercharges
• Instantons on the 5-sphere and M5-branes
• Approaching conformal window of $O(n)\times O(m)$ symmetric Landau-Ginzburg models from conformal bootstrap
• Eikonalization of Conformal Blocks
• A Non-Abelian Self-Dual Gauge Theory in 5+1 Dimensions
• $\mathcal{N}=1$ Superconformal Blocks for General Scalar Operators
• Superconformal Partition Functions and Non-perturbative Topological Strings
• General Three-Point Functions in 4D CFT
• Generalized bootstrap equations for N=4 SCFT
• JuliBootS: a hands-on guide to the conformal bootstrap
• The Superconformal Index of the (2,0) Theory with Defects
• Bounds on OPE Coefficients in 4D Conformal Field Theories
• Conformal Bootstrap Approach to O(N) Fixed Points in Five Dimensions
• Higher Derivative Terms, Toroidal Compactification, and Weyl Anomalies in Six-Dimensional (2,0) Theories
• Supersymmetric States in M5/M2 CFTs
• Embedding vs. 6D twistors

Cited by in corpus (125)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Precision Islands in the Ising and $O(N)$ Models
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• A Mellin space approach to the conformal bootstrap
• Carving out OPE space and precise $O(2)$ model critical exponents
• Vertex operator algebras, Higgs branches, and modular differential equations
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• $\mathcal{N}=4$ Super-Yang-Mills Correlators at Strong Coupling from String Theory and Localization
• A Proof of the Conformal Collider Bounds
• Weight Shifting Operators and Conformal Blocks
• S-folds and 4d N=3 superconformal field theories
• Bootstrapping the half-BPS line defect
• Universal anomalous dimensions at large spin and large twist
• Bootstrapping $\mathcal{N}=2$ chiral correlators
• Where is String Theory?
• Top Down Approach to 6D SCFTs
• Five dimensional $O(N)$-symmetric CFTs from conformal bootstrap
• Bootstrapping SCFTs with Four Supercharges
• Dispersive CFT Sum Rules
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Deformation quantization and superconformal symmetry in three dimensions
• The 3d Stress-Tensor Bootstrap
• Approaching conformal window of $O(n)\times O(m)$ symmetric Landau-Ginzburg models from conformal bootstrap
• Conformal Collider Physics from the Lightcone Bootstrap
• Projectors and seed conformal blocks for traceless mixed-symmetry tensors
• More $\mathcal{N}=4$ superconformal bootstrap
• Eikonalization of Conformal Blocks
• Radial expansion for spinning conformal blocks
• Probing thermality beyond the diagonal
• Solving M-theory with the Conformal Bootstrap
• Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions)
• One-loop amplitudes in $Ad{S}_5\times S^5$ supergravity from $\mathcal{N}=4$ SYM at strong coupling
• $\mathcal{N}=1$ Superconformal Blocks for General Scalar Operators
• Geometric constraints on the space of N=2 SCFTs I: physical constraints on relevant deformations
• PyCFTBoot: A flexible interface for the conformal bootstrap
• Bootstrapping Mixed Correlators in the Five Dimensional Critical O(N) Models
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
• Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6d $(2,0)$ theories
• Dimensional Reduction for Conformal Blocks
• A Semidefinite Program Solver for the Conformal Bootstrap
• Casimir recursion relations for general conformal blocks
• Decoding a Three-Dimensional Conformal Manifold
• The M-theory Archipelago
• $\mathcal{N}=2$ central charge bounds from $2d$ chiral algebras
• Generalized bootstrap equations for N=4 SCFT
• All Tree-Level Correlators for M-theory on $Ad{S}_7\times S^4$
• M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture
• (2,2) Superconformal Bootstrap in Two Dimensions
• Simplifying large spin bootstrap in Mellin space
• Non-Abelian Binding Energies from the Lightcone Bootstrap
• JuliBootS: a hands-on guide to the conformal bootstrap
• Scalar CFTs and Their Large N Limits
• Long Multiplet Bootstrap
• 3D CFT Archipelago from Single Correlator Bootstrap
• Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects
• Bootstrapping boundary-localized interactions II: Minimal models at the boundary
• Finite-$N$ corrections to the M-brane indices
• ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion
• Unitarity and positivity constraints for CFT at large central charge
• 6d (2,0) and M-theory at 1-loop
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• Bootstrap bound for conformal multi-flavor QCD on lattice
• Bootstrap experiments on higher dimensional CFTs
• Geometric constraints on the space of N=2 SCFTs III: enhanced Coulomb branches and central charges
• N=4 Superconformal Bootstrap of the K3 CFT
• Wilson Surface Central Charge from Holographic Entanglement Entropy
• Toda Theory From Six Dimensions
• Geometric constraints on the space of N=2 SCFTs II: Construction of special Kähler geometries and RG flows
• Inverse Bootstrapping Conformal Field Theories
• Conformal bootstrap bounds for the $U(1)$ Dirac spin liquid and $N=7$ Stiefel liquid
• Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach
• 6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• M-theory Beyond The Supergravity Approximation
• A search for minimal 4d N=1 SCFT
• Progress and prospects of lattice supersymmetry
• 6D (2,0) Bootstrap with soft-Actor-Critic
• Charting the space of 3D CFTs with a continuous global symmetry
• More on holographic correlators: Twisted and dimensionally reduced structures
• Mixed OPEs in $\mathcal{N}=2$ Superconformal Theories
• Five-Dimensional Non-Lorentzian Conformal Field Theories and their Relation to Six-Dimensions
• ${\varphi }^3$ theory with $F_4$ flavor symmetry in $6-2\epsilon$ dimensions: 3-loop renormalization and conformal bootstrap
• Supersymmetric Renyi Entropy and Weyl Anomalies in Six-Dimensional (2,0) Theories
• Bootstrapping $O(N)$ Vector Models with Four Supercharges in $3\le d\le 4$
• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• ABJ Correlators with Weakly Broken Higher Spin Symmetry
• Perturbative search for dead-end CFTs
• Lessons from M2's and Hopes for M5's
• Anomalous dimensions of spinning operators from conformal symmetry
• Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry
• Revisiting instanton corrections to the Konishi multiplet
• Bootstrapping Coulomb and Higgs branch operators
• Type-B Anomaly Matching and the 6D (2,0) Theory
• Differential operators for superconformal correlation functions
• Regge trajectories for the (2,0) theories
• The Epsilon-Expansion from Conformal Field Theory
• Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory
• 2d small N=4 Long-multiplet superconformal block
• Lessons from crossing symmetry at large N
• Pure anti-de Sitter supergravity and the conformal bootstrap
• $\mathcal{N}=(1,0)$ Anomaly Multiplet Relations in Six Dimensions
• Universal Bounds on Operator Dimensions in General 2D Conformal Field Theories
• A CFT Distance Conjecture
• Super-Spin Chains for 6D SCFTs
• (No) Bootstrap for the Fractal Ising Model
• Bootstrapping (D, D) Conformal Matter
• Five-Dimensional Path Integrals for Six-Dimensional Conformal Field Theories
• Weyl Anomaly and Vacuum Magnetization Current of M5-brane in Background Flux
• Comments on chiral algebras and $\Omega$-deformations
• Simplicity of AdS Supergravity at One Loop
• Deconstructing Conformal Blocks in 4D CFT
• Superconformal blocks in diverse dimensions and $BC$ symmetric functions
• Superconformal Partial Waves for Stress-tensor Multiplet Correlator in $4D$ $\mathcal{N}=2$ SCFTs
• Universal Bounds in Even-Spin CFTs
• Superconformal Block from Holographic Geometry
• Lectures on chiral algebras of $\mathcal{N}⩾2$ superconformal field theories
• M5-brane prongs, string soliton bound states and wall-crossing
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories
• Perturbative Unitarity Calls for An Action
• From Large to Small $\mathcal{N}=(4,4)$ Superconformal Surface Defects in Holographic 6d SCFTs
• Light cone OPE in a CFT with lowest twist scalar primary
• Two applications of the analytic conformal bootstrap: A quick tour guide
• Analytic Studies of Fermions in the Conformal Bootstrap
• Superconformal blocks for stress-tensor and chiral operators for 4D $\mathcal{N}=2$ superconformal field theories