A Semidefinite Program Solver for the Conformal Bootstrap

Abstract

We introduce SDPB: an open-source, parallelized, arbitrary-precision semidefinite program solver, designed for the conformal bootstrap. SDPB significantly outperforms less specialized solvers and should enable many new computations. As an example application, we compute a new rigorous high-precision bound on operator dimensions in the 3d Ising CFT, ${\Delta }_{\sigma }=0.518151(6)$, ${\Delta }_{\epsilon }=1.41264(6)$.

34 pages, 3 figures, and 3500 lines of C++

References in corpus (36)

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Cited by in corpus (37)

• Precision Islands in the Ising and $O(N)$ Models
• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• Conformal Invariance in the Long-Range Ising Model
• Bootstrapping $\mathcal{N}=2$ chiral correlators
• Fractal dimensions of self-avoiding walks and Ising high-temperature graphs in 3D conformal bootstrap
• Conformal Collider Physics from the Lightcone Bootstrap
• Eikonalization of Conformal Blocks
• Radial expansion for spinning conformal blocks
• Solving M-theory with the Conformal Bootstrap
• PyCFTBoot: A flexible interface for the conformal bootstrap
• Integrability and Conformal Bootstrap: One Dimensional Defect CFT
• Bootstrapping the long-range Ising model in three dimensions
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block
• Remarks on the Convergence Properties of the Conformal Block Expansion
• Non-Abelian Binding Energies from the Lightcone Bootstrap
• (2,2) Superconformal Bootstrap in Two Dimensions
• ${\mathbb{Z}}_N$ Symmetries, Anomalies, and the Modular Bootstrap
• Modular Constraints on Conformal Field Theories with Currents
• Crossing Kernels for Boundary and Crosscap CFTs
• N=4 Superconformal Bootstrap of the K3 CFT
• Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach
• The S-matrix Bootstrap III: Higher Dimensional Amplitudes
• The unitary subsector of generalized minimal models
• Extremal bootstrapping: go with the flow
• Modular Bootstrap Revisited
• New method for the conformal bootstrap with OPE truncations
• ${\varphi }^3$ theory with $F_4$ flavor symmetry in $6-2\epsilon$ dimensions: 3-loop renormalization and conformal bootstrap
• Conformal Bootstrap Signatures of the Tricritical Ising Universality Class
• The Epsilon-Expansion from Conformal Field Theory
• Bootstrap Bounds on Closed Hyperbolic Manifolds
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• Bootstrapping Pure Quantum Gravity in AdS3
• Quantum algorithms for conformal bootstrap
• Genus Two Modular Bootstrap
• Superconformal Partial Waves for Stress-tensor Multiplet Correlator in $4D$ $\mathcal{N}=2$ SCFTs
• The interface tension in the improved Blume-Capel model