Chiral Modular Bootstrap

Abstract

Using modular bootstrap we show the lightest primary fields of a unitary compact two dimensional conformal field theory(with $c,\bar{c}>1$) has a conformal weight $h_1\le \frac{c}{12}+\mathcal{O}(1)$.This implies that the upper bound on the dimension of the lightest primary fields depends on their spin. In particular if the set of lightest primary fields includes extremal or near extremal states whose spin to dimension ratio $\frac{j}{\Delta }\approx 1$, the corresponding dimension is $\Delta \le \frac{c}{12}+\mathcal{O}(1)$. From AdS/CFT correspondence, we obtain an upper bound on the spectrum of black hole in three dimensional gravity. Our results show that if the first primary fields have large spin, the corresponding three dimensional gravity has extremal or near extremal BTZ black hole.

15 pages, 2 figures

References in corpus (11)

• Quantum Gravity Partition Functions in Three Dimensions
• Meromorphic c=24 Conformal Field Theories
• A Universal Inequality for CFT and Quantum Gravity
• Constraints on 2d CFT partition functions
• Universal Bounds on Charged States in 2d CFT and 3d Gravity
• Fast Conformal Bootstrap and Constraints on 3d Gravity
• Constraints on Flavored 2d CFT Partition Functions
• Bounds on Operator Dimensions in 2D Conformal Field Theories
• Parity and the modular bootstrap
• Modular Constraints on Superconformal Field Theories
• Non-chiral 2d CFT with integer energy levels

Cited by in corpus (3)

• High Energy Modular Bootstrap, Global Symmetries and Defects
• Aspects of the S transformation Bootstrap
• Three Dimensional Pure Gravity and Generalized Hecke Operators