# 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 ($$k\overline{k}\ $$) 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.

- Authors:

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

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1502475

- Grant/Contract Number:
- SC0009988

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 2; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; Higher Spin Symmetry

### Citation Formats

```
Córdova, Clay, and Diab, Kenan. Universal bounds on operator dimensions from the average null energy condition. United States: N. p., 2018.
Web. doi:10.1007/jhep02(2018)131.
```

```
Córdova, Clay, & Diab, Kenan. Universal bounds on operator dimensions from the average null energy condition. United States. doi:10.1007/jhep02(2018)131.
```

```
Córdova, Clay, and Diab, Kenan. Wed .
"Universal bounds on operator dimensions from the average null energy condition". United States. doi:10.1007/jhep02(2018)131. https://www.osti.gov/servlets/purl/1502475.
```

```
@article{osti_1502475,
```

title = {Universal bounds on operator dimensions from the average null energy condition},

author = {Córdova, Clay and Diab, Kenan},

abstractNote = {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.},

doi = {10.1007/jhep02(2018)131},

journal = {Journal of High Energy Physics (Online)},

number = 2,

volume = 2018,

place = {United States},

year = {2018},

month = {2}

}

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Works referencing / citing this record:

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Higher spin ANEC and the space of CFTs

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Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*