Fast Conformal Bootstrap and Constraints on 3d Gravity

Abstract

The crossing equations of a conformal field theory can be systematically truncated to a finite, closed system of polynomial equations. In certain cases, solutions of the truncated equations place strict bounds on the space of all unitary CFTs. We describe the conditions under which this holds, and use the results to develop a fast algorithm for modular bootstrap in 2d CFT. We then apply it to compute spectral gaps to very high precision, find scaling dimensions for over a thousand operators, and extend the numerical bootstrap to the regime of large central charge, relevant to holography. This leads to new bounds on the spectrum of black holes in three-dimensional gravity. We provide numerical evidence that the asymptotic bound on the spectral gap from spinless modular bootstrap, at large central charge $c$, is ${\Delta }_1\lesssim c/9.1$.

31 pages, 5 figures

References in corpus (9)

• Holography from Conformal Field Theory
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Bounds on 4D Conformal and Superconformal Field Theories
• Poincare Series, 3D Gravity and CFT Spectroscopy
• Critical exponents of the 3d Ising and related models from Conformal Bootstrap
• String Universality for Permutation Orbifolds
• Charged structure constants from modularity

Cited by in corpus (1)

• Chiral Modular Bootstrap