We prove using invariance under the modular S- and ST-transformations
that every unitary two-dimensional conformal field theory (CFT) of only
even-spin operators (with no extended chiral algebra and with central charges
c,c~>1) contains a primary operator with dimension Ξ1β
satisfying 0<Ξ1β<(c+c~)/24+0.09280... After deriving both
analytical and numerical bounds, we discuss how to extend our methods to bound
higher conformal dimensions before deriving lower and upper bounds on the
number of primary operators in a given energy range. Using the AdS3β/CFT2β
dictionary, the bound on Ξ1β proves the lightest massive excitation in
appropriate theories of 3D matter and gravity with cosmological constant
Ξ<0 can be no heavier than 1/(8GNβ)+O(βΞβ); the bounds
on the number operators are related via AdS/CFT to the entropy of states in the
dual gravitational theory. In the flat-space approximation, the limiting mass
is exactly that of the lightest BTZ black hole.Comment: arXiv admin note: text overlap with arXiv:0902.2790 by other authors;
author note: this work is an extension of arXiv:0902.2790, please refer to it
for additional details..new version has corrected typos and reference