# Counting conformal correlators

## Abstract

We introduce simple group-theoretic techniques for classifying conformallyinvariant tensor structures. With them, we classify tensor structures of general n-point functions of non-conserved operators, and n ≥ 4-point functions of general conserved currents, with or without permutation symmetries, and in any spacetime dimension d. Our techniques are useful for bootstrap applications. The rules we derive simultaneously count tensor structures for flat-space scattering amplitudes in d + 1 dimensions.

- Authors:

- California Inst. of Technology, Pasadena (United States). Walter Burke Inst. for Theoretical Physics
- California Inst. of Technology, Pasadena (United States). Walter Burke Inst. for Theoretical Physics; Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences

- Publication Date:

- Research Org.:
- Inst. for Advanced Study, Princeton, NJ (United States); California Inst. of Technology, Pasadena (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1502434

- Grant/Contract Number:
- SC0009988; SC0011632

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- 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; Conformal and W Symmetry; Field Theories in Higher Dimensions; Space-Time Symmetries

### Citation Formats

```
Kravchuk, Petr, and Simmons-Duffin, David.
```*Counting conformal correlators*. United States: N. p., 2018.
Web. doi:10.1007/jhep02(2018)096.

```
Kravchuk, Petr, & Simmons-Duffin, David.
```*Counting conformal correlators*. United States. doi:10.1007/jhep02(2018)096.

```
Kravchuk, Petr, and Simmons-Duffin, David. Thu .
"Counting conformal correlators". United States. doi:10.1007/jhep02(2018)096. https://www.osti.gov/servlets/purl/1502434.
```

```
@article{osti_1502434,
```

title = {Counting conformal correlators},

author = {Kravchuk, Petr and Simmons-Duffin, David},

abstractNote = {We introduce simple group-theoretic techniques for classifying conformallyinvariant tensor structures. With them, we classify tensor structures of general n-point functions of non-conserved operators, and n ≥ 4-point functions of general conserved currents, with or without permutation symmetries, and in any spacetime dimension d. Our techniques are useful for bootstrap applications. The rules we derive simultaneously count tensor structures for flat-space scattering amplitudes in d + 1 dimensions.},

doi = {10.1007/jhep02(2018)096},

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

issn = {1029-8479},

number = 2,

volume = 2018,

place = {United States},

year = {2018},

month = {2}

}

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