Lightcone modular bootstrap and pure gravity
Abstract
We explore the large spin spectrum in twodimensional conformal field theories with a finite twist gap, using the modular bootstrap in the lightcone limit. By recursively solving the modular crossing equations associated with different P S L (2 ,Z ) elements, we identify the universal contribution to the density of large spin states from the vacuum in the dual channel. Our result takes the form of a sum over P S L (2 ,Z ) elements, whose leading term generalizes the usual Cardy formula to a wider regime. Rather curiously, the contribution to the density of states from the vacuum becomes negative in a specific limit, which can be canceled by that from a nonvacuum Virasoro primary whose twist is no bigger than c/1 1 6 . This suggests a new upper bound of c/1 1 6 on the twist gap in any c >1 compact, unitary conformal field theory with a vacuum, which would in particular imply that pure AdS_{3} gravity does not exist. We confirm this negative density of states in the pure gravity partition function by Maloney, Witten, and Keller. We generalize our discussion to theories with N =(1 ,1 ) supersymmetry and find similar results.
 Publication:

Physical Review D
 Pub Date:
 September 2019
 DOI:
 10.1103/PhysRevD.100.066029
 arXiv:
 arXiv:1906.04184
 Bibcode:
 2019PhRvD.100f6029B
 Keywords:

 High Energy Physics  Theory
 EPrint:
 31 pages, v2: added supersymmetric generalization