Modular Bootstrap Revisited

Abstract

We constrain the spectrum of two-dimensional unitary, compact conformal field theories with central charge c > 1 using modular bootstrap. Upper bounds on the gap in the dimension of primary operators of any spin, as well as in the dimension of scalar primaries, are computed numerically as functions of the central charge using semi-definite programming. Our bounds refine those of Hellerman and Friedan-Keller, and are in some cases saturated by known CFTs. In particular, we show that unitary CFTs with c < 8 must admit relevant deformations, and that a nontrivial bound on the gap of scalar primaries exists for c < 25. We also study bounds on the dimension gap in the presence of twist gaps, bounds on the degeneracy of operators, and demonstrate how "extremal spectra" which maximize the degeneracy at the gap can be determined numerically.

32 pages, 20 figures

References in corpus (13)

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• Bounds on Operator Dimensions in 2D Conformal Field Theories
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• Charged structure constants from modularity
• (2,2) Superconformal Bootstrap in Two Dimensions
• Scalar CFTs and Their Large N Limits
• Modular Constraints on Conformal Field Theories with Currents
• Bootstrapping holographic warped CFTs or: how I learned to stop worrying and tolerate negative norms
• Black holes from CFT: Universality of correlators at large c
• Classical Conformal Blocks and Accessory Parameters from Isomonodromic Deformations
• New method for the conformal bootstrap with OPE truncations
• Bounds on CFTs with $W_3$ algebras and AdS${}_3$ higher spin theories
• Bootstrapping Pure Quantum Gravity in AdS3
• Genus Two Modular Bootstrap
• Bootstrapping Chiral CFTs at Genus Two