Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions)

Abstract

We bootstrap $\mathcal{N}=(1,0)$ superconformal field theories in six dimensions, by analyzing the four-point function of flavor current multiplets. Assuming $E_8$ flavor group, we present universal bounds on the central charge $C_T$ and the flavor central charge $C_J$. Based on the numerical data, we conjecture that the rank-one E-string theory saturates the universal lower bound on $C_J$, and numerically determine the spectrum of long multiplets in the rank-one E-string theory. We comment on the possibility of solving the higher-rank E-string theories by bootstrap and thereby probing M-theory on AdS${}_7\times {\mathrm{S}}^4$/${\mathbb{Z}}_2$.

arXiv comment59 pages, 10 figures, 4 tables; v2-v5: typos corrected, references added

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• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
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• Universal Features of BPS Strings in Six-dimensional SCFTs
• Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey
• Casimir recursion relations for general conformal blocks
• The M-theory Archipelago
• Fission, Fusion, and 6D RG Flows
• M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture
• AdS${}_7$/CFT${}_6$ with orientifolds
• Revisiting the classifications of 6d SCFTs and LSTs
• 4D Gauge Theories with Conformal Matter
• One-loop Gluon Amplitudes in AdS
• 6d surface defects from massive type IIA
• Searching for gauge theories with the conformal bootstrap
• Scaling the semidefinite program solver SDPB
• Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
• On Mellin Amplitudes in SCFTs with Eight Supercharges
• New Methods for Conformal Correlation Functions
• Inverse Bootstrapping Conformal Field Theories
• 6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains
• The unitary subsector of generalized minimal models
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• A 3d disordered superconformal fixed point
• New method for the conformal bootstrap with OPE truncations
• AdS super gluon scattering up to two loops: A position space approach
• Superconformal Blocks: General Theory
• Green-Schwarz Automorphisms and 6D SCFTs
• Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry
• Bootstrapping Coulomb and Higgs branch operators
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• 3d N=4 Bootstrap and Mirror Symmetry
• An Automated Generation of Bootstrap Equations for Numerical Study of Critical Phenomena
• 2d small N=4 Long-multiplet superconformal block
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• $\mathcal{N}=(1,0)$ Anomaly Multiplet Relations in Six Dimensions
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• Super-Spin Chains for 6D SCFTs
• Bootstrapping (D, D) Conformal Matter
• Punctures and Dynamical Systems
• autoboot: A generator of bootstrap equations with global symmetry
• Harmonic Analysis in d-dimensional Superconformal Field Theory
• Crossing Symmetry for Long Multiplets in 4D $\mathcal{N}=1$ SCFTs
• Analytic Studies of Fermions in the Conformal Bootstrap