2013/12/31 by Joshua D. Qualls, Alfred D. Shapere · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/jhep05(2014)091
Corrected typos; revised arguments (adding detail) for clarity, results unchanged
arxiv created 2014/04/30 · arxiv updated 2015/06/18
We extend the work of Hellerman (arxiv:0902.2790) to derive an upper bound on the conformal dimension Δ2 of the next-to-lowest nontrival primary operator in unitary two-dimensional conformal field theories without chiral primary operators. The bound we find is of the same form as found for Δ1: Δ2 ≤ ctot/12 + O(1). We find a similar bound on the conformal dimension Δ3, and present a method for deriving bounds on Δn for any n, under slightly modified assumptions. For asymptotically large ctot and fixed n, we show that Δn ≤ \fracctot12+O(1). We conclude with a brief discussion of the gravitational implications of these results.