Extremal bootstrapping: go with the flow

Abstract

The extremal functional method determines approximate solutions to the constraints of crossing symmetry, which saturate bounds on the space of unitary CFTs. We show that such solutions are characterized by extremality conditions, which may be used to flow continuously along the boundaries of parameter space. Along the flow there is generically no further need for optimization, which dramatically reduces computational requirements, bringing calculations from the realm of computing clusters to laptops. Conceptually, extremality sheds light on possible ways to bootstrap without positivity, extending the method to non-unitary theories, and implies that theories saturating bounds, and especially those sitting at kinks, have unusually sparse spectra. We discuss several applications, including the first high-precision bootstrap of a non-unitary CFT.

35+5 pages and lots of nice figures

References in corpus (4)

• 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
• A Semidefinite Program Solver for the Conformal Bootstrap
• JuliBootS: a hands-on guide to the conformal bootstrap

Cited by in corpus (13)

• The S-matrix Bootstrap II: Two Dimensional Amplitudes
• A tauberian theorem for the conformal bootstrap
• Crossing Symmetry in Alpha Space
• Bootstrapping the long-range Ising model in three dimensions
• Casimir recursion relations for general conformal blocks
• Bootstrapping Mixed Correlators in 4D $\mathcal{N}=1$ SCFTs
• Anomalous Dimensions in the WF O($N$) Model with a Monodromy Line Defect
• Crossing Kernels for Boundary and Crosscap CFTs
• Inverse Bootstrapping Conformal Field Theories
• The unitary subsector of generalized minimal models
• New method for the conformal bootstrap with OPE truncations
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• Conformal Bootstrap with Reinforcement Learning