Universal bounds on operator dimensions from the average null energy condition

Córdova, Clay; Diab, Kenan

doi:10.1007/jhep02(2018)131

Title: Universal bounds on operator dimensions from the average null energy condition

Journal Article · 20 February 2018 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep02(2018)131 · OSTI ID:1502475

Córdova, Clay ^[1];

^[2]

Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Inst. for Advanced Study, Pinceton, NJ (United States)
Princeton Univ., NJ (United States). Dept. of Physics

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 ($$k\overline{k}\ $$) 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 ($$k\overline{k}\ $$) and scaling dimension Δ satisfy Δ ≥ max{$$k\overline{k}\ $$}. If |$$k-\overline{k}\ $$| > 4 , this is stronger than the unitarity bound.

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Research Organization:: Inst. for Advanced Study, Princeton, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0009988

OSTI ID:: 1502475

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 2 Vol. 2018; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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