Solving M-theory with the Conformal Bootstrap

Abstract

We use the conformal bootstrap to perform a precision study of 3d maximally supersymmetric ($\mathcal{N}=8$) SCFTs that describe the IR physics on $N$ coincident M2-branes placed either in flat space or at a $\C^4/\Z_2$ singularity. First, using the explicit Lagrangians of ABJ(M) \cite{Aharony:2008ug,Aharony:2008gk} and recent supersymmetric localization results, we calculate certain half and quarter-BPS OPE coefficients, both exactly at small $N$, and approximately in a large $N$ expansion that we perform to all orders in $1/N$. Comparing these values with the numerical bootstrap bounds leads us to conjecture that some of these theories obey an OPE coefficient minimization principle. We then use this conjecture as well as the extremal functional method to reconstruct the first few low-lying scaling dimensions and OPE coefficients for both protected and unprotected multiplets that appear in the OPE of two stress tensor multiplets for all values of $N$. We also calculate the half and quarter-BPS operator OPE coefficients in the $SU(2{)}_k\times SU(2{)}_{-k}$ BLG theory for all values of the Chern-Simons coupling $k$, and show that generically they do not obey the same OPE coefficient minimization principle.

arXiv comment30 pages, 5 figures, v2 submitted for publication

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• Where is String Theory?
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• The M-Theory S-Matrix From ABJM: Beyond 11D Supergravity
• On Superconformal Four-Point Mellin Amplitudes in Dimension $d>2$
• Decoding a Three-Dimensional Conformal Manifold
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• The M-theory Archipelago
• M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture
• Large $N$ Partition Functions of the ABJM Theory
• Searching for gauge theories with the conformal bootstrap
• All Holographic Four-Point Functions in All Maximally Supersymmetric CFTs
• ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion
• 3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
• Scaling the semidefinite program solver SDPB
• Squashing, Mass, and Holography for 3d Sphere Free Energy
• 6d (2,0) and M-theory at 1-loop
• On Mellin Amplitudes in SCFTs with Eight Supercharges
• AdS${}_4$/CFT${}_3$ for Unprotected Operators
• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
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• New method for the conformal bootstrap with OPE truncations
• ABJ Correlators with Weakly Broken Higher Spin Symmetry
• Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry
• Differential operators for superconformal correlation functions
• Bootstrapping Coulomb and Higgs branch operators
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• 3d N=4 Bootstrap and Mirror Symmetry
• One-Dimensional Sectors From the Squashed Three-Sphere
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• Higher-Derivative Supergravity, AdS${}_4$ Holography, and Black Holes
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• Fermi-gas correlators of ADHM theory and triality symmetry
• Generating functions for Higgs/Coulomb branch operators from 1d-3d cohomological equivalence
• Analytic Studies of Fermions in the Conformal Bootstrap
• Holographic Wilson Loop One-point Functions in ABJM Theory