## General bootstrap equations in 4D CFTs

## Abstract

We provide a framework for generic 4D conformal bootstrap computations. It is based on the unification of two independent approaches, the covariant (embedding) formalism and the non-covariant (conformal frame) formalism. We construct their main ingredients (tensor structures and differential operators) and establish a precise connection between them. We supplement the discussion by additional details like classification of tensor structures of n-point functions, normalization of 2-point functions and seed conformal blocks, Casimir differential operators and treatment of conserved operators and permutation symmetries. Lastly, we implement our framework in a Mathematica package and make it freely available.

- Authors:

- Ecole Polytechnique Federale Lausanne (EFPL), Lausanne (Switzlerland)
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste (Italy); Italian National Institute of Nuclear Physics (INFN), Trieste (Italy)
- California Inst. of Technology (CalTech), Pasadena, CA (United States)

- Publication Date:

- Research Org.:
- California Inst. of Tech., Pasadena (United States)

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

- OSTI Identifier:
- 1499644

- Grant/Contract Number:
- SC0011632

- 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: 1; 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, Nonperturbative Effects

### Citation Formats

```
Cuomo, Gabriel Francisco, Karateev, Denis, and Kravchuk, Petr. General bootstrap equations in 4D CFTs. United States: N. p., 2018.
Web. doi:10.1007/jhep01(2018)130.
```

```
Cuomo, Gabriel Francisco, Karateev, Denis, & Kravchuk, Petr. General bootstrap equations in 4D CFTs. United States. doi:10.1007/jhep01(2018)130.
```

```
Cuomo, Gabriel Francisco, Karateev, Denis, and Kravchuk, Petr. Thu .
"General bootstrap equations in 4D CFTs". United States. doi:10.1007/jhep01(2018)130. https://www.osti.gov/servlets/purl/1499644.
```

```
@article{osti_1499644,
```

title = {General bootstrap equations in 4D CFTs},

author = {Cuomo, Gabriel Francisco and Karateev, Denis and Kravchuk, Petr},

abstractNote = {We provide a framework for generic 4D conformal bootstrap computations. It is based on the unification of two independent approaches, the covariant (embedding) formalism and the non-covariant (conformal frame) formalism. We construct their main ingredients (tensor structures and differential operators) and establish a precise connection between them. We supplement the discussion by additional details like classification of tensor structures of n-point functions, normalization of 2-point functions and seed conformal blocks, Casimir differential operators and treatment of conserved operators and permutation symmetries. Lastly, we implement our framework in a Mathematica package and make it freely available.},

doi = {10.1007/jhep01(2018)130},

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

number = 1,

volume = 2018,

place = {United States},

year = {2018},

month = {1}

}

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