Universal bounds on operator dimensions from the average null energy condition

Abstract

We show that the average null energy condition implies novel lower bounds on the scaling dimensions of highly-chiral primary operators in four-dimensional conformal field theories. Denoting the spin of an operator by a pair of integers (kk¯) specifying the transformations under chiral su(2) rotations, we explicitly demonstrate these new bounds for operators transforming in (k, 0) and (k, 1) representations for sufficiently large k. Based on these calculations, along with intuition from free field theory, we conjecture that in any unitary conformal field theory, primary local operators of spin (kk¯) and scaling dimension Δ satisfy Δ≥ max {kk¯}. If | k− k¯ | > 4 , this is stronger than the unitarity bound.