Modular Bootstrap Revisited
arXiv:1608.06241
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 (5)
- Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
- Three-Dimensional Gravity Revisited
- Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
- Poincare Series, 3D Gravity and CFT Spectroscopy
- A Semidefinite Program Solver for the Conformal Bootstrap
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