3D CFT Archipelago from Single Correlator Bootstrap

Abstract

We show that the scaling dimensions of lowest operators in conformal field theories (CFTs) can be isolated in small and closed regions from single correlator bootstrap. We find the conserved currents play crucial roles in bootstrapping the crossing equation. By imposing a mild gap between the scaling dimensions of the conserved current and its next operator, the scaling dimensions of lowest operators are forced to lie in small isolated regions, i.e., these CFTs can be almost fixed by few lowest operators in certain channels. For CFTs with extended supersymmetry, the single correlator crossing equation involves several conserved or shorted operators and by imposing gaps in these sectors it is possible to isolate different CFTs. Specifically, we bootstrap the isolated regions corresponding to the 3D Ising model, $O(N)$ vector model, $N=1,2$ supersymmetric Ising models by introducing mild gaps in certain sectors with conserved or shorted operators.

4 figures, 5 pages

References in corpus (7)

• Bounds on 4D Conformal and Superconformal Field Theories
• A Mellin space approach to the conformal bootstrap
• Conformal Bootstrap in Mellin Space
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Analytic Bounds and Emergence of ${\text{AdS}}_2$ Physics from the Conformal Bootstrap
• Solving CFTs with Weakly Broken Higher Spin Symmetry
• Long strings and chiral primaries in the hybrid formalism

Cited by in corpus (20)

• Carving out OPE space and precise $O(2)$ model critical exponents
• Bootstrapping the long-range Ising model in three dimensions
• Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories
• The M-theory Archipelago
• Scalar CFTs and Their Large N Limits
• Analytic and Numerical Bootstrap of CFTs with $O(m)\times O(n)$ Global Symmetry in 3D
• Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories II
• Mixed Scalar-Current bootstrap in three dimensions
• The unitary subsector of generalized minimal models
• Bootstrapping traceless symmetric $O(N)$ scalars
• New method for the conformal bootstrap with OPE truncations
• A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions
• Bootstrapping Coulomb and Higgs branch operators
• Navigating through the O(N) archipelago
• The tricritical Ising CFT and conformal bootstrap
• Superconformal Partial Waves for Stress-tensor Multiplet Correlator in $4D$ $\mathcal{N}=2$ SCFTs
• Bootstrapping mixed correlators in the 2D Ising model
• Analytic Studies of Fermions in the Conformal Bootstrap
• Conformal Bootstrap with Duality-Inspired Fusion Rule
• Superconformal blocks for stress-tensor and chiral operators for 4D $\mathcal{N}=2$ superconformal field theories