The M-theory Archipelago

Abstract

We combine supersymmetric localization results and the numerical conformal bootstrap technique to study the 3d maximally supersymmetric ($\mathcal{N}=8$) CFT on $N$ coincident M2-branes (the $U(N{)}_k\times U(N{)}_{-k}$ ABJM theory at Chern-Simons level $k=1$). In particular, we perform a mixed correlator bootstrap study of the superconformal primaries of the stress tensor multiplet and of the next possible lowest-dimension half-BPS multiplet that is allowed by 3d $\mathcal{N}=8$ superconformal symmetry. Of all known 3d $\mathcal{N}=8$ SCFTs, the $k=1$ ABJM theory is the only one that contains both types of multiplets in its operator spectrum. By imposing the values of the short OPE coefficients that can be computed exactly using supersymmetric localization, we are able to derive precise islands in the space of semi-short OPE coefficients for an infinite number of such coefficients. We find that these islands decrease in size with increasing $N$. More generally, we also analyze 3d $\mathcal{N}=8$ SCFT that contain both aforementioned multiplets in their operator spectra without inputing any additional information that is specific to ABJM theory. For such theories, we compute upper and lower bounds on the semi-short OPE coefficients as well as upper bounds on the scaling dimension of the lowest unprotected scalar operator. These latter bounds are more constraining than the analogous bounds previously derived from a single correlator bootstrap of the stress tensor multiplet. This leads us to conjecture that the $U(N{)}_2\times U(N+1{)}_{-2}$ ABJ theory, and not the $k=1$ ABJM theory, saturates the single correlator bounds.

arXiv comment42 pages plus appendices, 13 figures, v2 typos fixed

References in corpus (59)

• 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
• Bounding scalar operator dimensions in 4D CFT
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Modeling Multiple M2's
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Comments on Multiple M2-branes
• Fractional M2-branes
• Infinite Chiral Symmetry in Four Dimensions
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Precision Islands in the Ising and $O(N)$ Models
• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• Bootstrapping Mixed Correlators in the 3D Ising Model
• ABJM theory as a Fermi gas
• Bounds on 4D Conformal and Superconformal Field Theories
• Carving Out the Space of 4D CFTs
• The N=4 Superconformal Bootstrap
• Bootstrapping Conformal Field Theories with the Extremal Functional Method
• Comments on the Bagger-Lambert theory and multiple M2-branes
• Supersymmetric Field Theories on Three-Manifolds
• The $(2,0)$ superconformal bootstrap
• Bootstrapping the O(N) Archipelago
• N=2 supersymmetric theories on squashed three-sphere
• Superconformal Ward Identities and their Solution
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• The $\mathcal{N}=2$ superconformal bootstrap
• Bootstrapping the half-BPS line defect
• Bootstrapping $\mathcal{N}=2$ chiral correlators
• N = 8 Superconformal Chern--Simons Theories
• On Four-Point Functions of Half-BPS Operators in General Dimensions
• Deformation quantization and superconformal symmetry in three dimensions
• Bounds on $\mathcal{N}=1$ Superconformal Theories with Global Symmetries
• Bootstrapping $\mathcal{N}=3$ superconformal theories
• More $\mathcal{N}=4$ superconformal bootstrap
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• Solving M-theory with the Conformal Bootstrap
• The M-Theory S-Matrix From ABJM: Beyond 11D Supergravity
• Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions)
• On Superconformal Four-Point Mellin Amplitudes in Dimension $d>2$
• Instanton effects in ABJM theory with general R-charge assignments
• Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey
• Bootstrapping Mixed Correlators in the Five Dimensional Critical O(N) Models
• Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories
• Decoding a Three-Dimensional Conformal Manifold
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• Relating U(N)xU(N) to SU(N)xSU(N) Chern-Simons Membrane theories
• Accidental Symmetries and the Conformal Bootstrap
• New and old N=8 superconformal field theories in three dimensions
• On Superconformal Characters and Partition Functions in Three Dimensions
• Bootstrapping Mixed Correlators in 4D $\mathcal{N}=1$ SCFTs
• Bootstrapping the Minimal 3D SCFT
• Universal properties of superconformal OPEs for 1/2 BPS operators in $3\le D\le 6$
• 3D CFT Archipelago from Single Correlator Bootstrap
• Coulomb Branch Quantization and Abelianized Monopole Bubbling
• Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
• AdS${}_4$/CFT${}_3$ for Unprotected Operators
• A New Duality Between $\mathcal{N}=8$ Superconformal Field Theories in Three Dimensions

Cited by in corpus (34)

• Carving out OPE space and precise $O(2)$ model critical exponents
• Dispersive CFT Sum Rules
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Gluon Scattering in AdS from CFT
• Large $N$ Partition Functions of the ABJM Theory
• New Developments in the Numerical Conformal Bootstrap
• Bootstrapping $N_f=4$ conformal QED${}_3$
• Searching for gauge theories with the conformal bootstrap
• ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion
• 3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
• Mixed Scalar-Current bootstrap in three dimensions
• Bootstrapping 4d $\mathcal{N}=2$ gauge theories: the case of SQCD
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• Bootstrapping traceless symmetric $O(N)$ scalars
• More on holographic correlators: Twisted and dimensionally reduced structures
• ABJ Correlators with Weakly Broken Higher Spin Symmetry
• Bootstrapping Coulomb and Higgs branch operators
• Differential operators for superconformal correlation functions
• Analytic and numerical bootstrap for the long-range Ising model
• 3d N=4 Bootstrap and Mirror Symmetry
• One-Dimensional Sectors From the Squashed Three-Sphere
• The topological line of ABJ(M) theory
• Bootstrapping mixed correlators in $\mathcal{N}=4$ Super Yang-Mills
• Pure anti-de Sitter supergravity and the conformal bootstrap
• Holographic S-fold theories at one loop
• OPE coefficients in Argyres-Douglas theories
• Bootstrapping (D, D) Conformal Matter
• Conformal Bootstrap Deformations
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories
• Fermi-gas correlators of ADHM theory and triality symmetry
• The Holographic Contributions to the Sphere Free Energy
• Exact expressions for $n$-point maximal $U(1{)}_Y$-violating integrated correlators in $SU(N)$ $\mathcal{N}=4$ SYM