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arXiv · 1712.01089

Universal Bounds on Operator Dimensions from the Average Null Energy Condition

Clay Cordova·Kenan Diab
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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 $(k,\bar{k})$ specifying the transformations under chiral $\frak{su}(2)$ 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 $(k,\bar{k})$ and scaling dimension $\Delta$ satisfy $\Delta \geq \text{max}\{k,\bar{k}\}.$ If $|k-\bar{k}| > 4$, this is stronger than the unitarity bound.

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Clay Cordova, Kenan Diab. 2017-12-04. Universal Bounds on Operator Dimensions from the Average Null Energy Condition. https://doi.org/10.1007/jhep02(2018)131

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