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.

30 pages, 5 figures, v2 submitted for publication

References in corpus (21)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Fractional M2-branes
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• 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
• Comments on the Bagger-Lambert theory and multiple M2-branes
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• N = 8 Superconformal Chern--Simons Theories
• Bootstrapping $O(N)$ Vector Models in $4<d<6$
• Exact results on ABJ theory and the refined topological string
• Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey
• A Semidefinite Program Solver for the Conformal Bootstrap
• Monopole Operators in $U(1)$ Chern-Simons-Matter Theories
• A 2d/1d Holographic Duality
• Exact results in N=8 Chern-Simons-matter theories and quantum geometry
• BLG theories at low values of Chern-Simons coupling

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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
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• More on holographic correlators: Twisted and dimensionally reduced structures
• Comments on ABJM free energy on $S^3$ at large $N$ and perturbative expansions in M-theory and string theory
• 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
• Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory
• 3d N=4 Bootstrap and Mirror Symmetry
• One-Dimensional Sectors From the Squashed Three-Sphere
• An Automated Generation of Bootstrap Equations for Numerical Study of Critical Phenomena
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• Conformal bounds in three dimensions from entanglement entropy
• Pure anti-de Sitter supergravity and the conformal bootstrap
• SU(N) q-Toda equations from mass deformed ABJM theory
• Bootstrapping (D, D) Conformal Matter
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• autoboot: A generator of bootstrap equations with global symmetry
• Higher-Derivative Supergravity, AdS${}_4$ Holography, and Black Holes
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories
• The Holographic Contributions to the Sphere Free Energy
• 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