# Mellin bootstrap for scalars in generic dimension

## Abstract

We use the recently developed framework of the Mellin bootstrap to study perturbatively free scalar CFTs in arbitrary dimensions. This approach uses the crossing-symmetric Mellin space formulation of correlation functions to generate algebraic bootstrap equations by demanding that only physical operators contribute to the OPE. We find that there are no perturbatively interacting CFTs with only fundamental scalars in *d* > 6 dimensions (to at least second order in the perturbation). Our results can be seen as a modest step towards understanding the space of interacting CFTs in *d* > 6 and are consistent with the intuition that no such CFTs exist.

- Authors:

- Univ. of Michigan, Ann Arbor, MI (United States). Dept. of Physics and Leinweber Center for Theoretical Physics

- Publication Date:

- Research Org.:
- Univ. of Michigan, Ann Arbor, MI (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1507007

- Grant/Contract Number:
- FG02-95ER40899

- 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: 6; 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; Field Theories in Higher Dimensions

### Citation Formats

```
Golden, John, and Mayerson, Daniel R. Mellin bootstrap for scalars in generic dimension. United States: N. p., 2018.
Web. doi:10.1007/jhep06(2018)066.
```

```
Golden, John, & Mayerson, Daniel R. Mellin bootstrap for scalars in generic dimension. United States. doi:10.1007/jhep06(2018)066.
```

```
Golden, John, and Mayerson, Daniel R. Wed .
"Mellin bootstrap for scalars in generic dimension". United States. doi:10.1007/jhep06(2018)066. https://www.osti.gov/servlets/purl/1507007.
```

```
@article{osti_1507007,
```

title = {Mellin bootstrap for scalars in generic dimension},

author = {Golden, John and Mayerson, Daniel R.},

abstractNote = {We use the recently developed framework of the Mellin bootstrap to study perturbatively free scalar CFTs in arbitrary dimensions. This approach uses the crossing-symmetric Mellin space formulation of correlation functions to generate algebraic bootstrap equations by demanding that only physical operators contribute to the OPE. We find that there are no perturbatively interacting CFTs with only fundamental scalars in d > 6 dimensions (to at least second order in the perturbation). Our results can be seen as a modest step towards understanding the space of interacting CFTs in d > 6 and are consistent with the intuition that no such CFTs exist.},

doi = {10.1007/jhep06(2018)066},

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

number = 6,

volume = 2018,

place = {United States},

year = {2018},

month = {6}

}

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