## Double-trace deformations of conformal correlations

## Abstract

Large *N* conformal field theories often admit unitary renormalization group flows triggered by double-trace deformations. We compute the change in scalar four-point functions under double-trace flow, to leading order in 1/ *N*. This has a simple dual in AdS, where the flow is implemented by a change of boundary conditions, and provides a physical interpretation of single-valued conformal partial waves. We extract the change in the conformal dimensions and three-point coefficients of infinite families of double-trace composite operators. Some of these quantities are found to be sign-definite under double-trace flow. As an application, we derive anomalous dimensions of spinning double-trace operators comprised of non-singlet constituents in the *O*( *N*) vector model.

- Authors:

- Princeton Univ., Princeton, NJ (United States). Dept. of Physics
- Princeton Univ., Princeton, NJ (United States). Dept. of Physics; Inst. of Theoretical and Experimental Physics (ITEP), Moscow (Russian Federation)
- Princeton Univ., Princeton, NJ (United States). Dept. of Physics; California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics

- Publication Date:

- Research Org.:
- Princeton Univ., NJ (United States); California Inst. of Tech., Pasadena, CA (United States)

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

- OSTI Identifier:
- 1507423

- Grant/Contract Number:
- FG02-91ER40671; SC0011632; PHY-1620542; 488657

- 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; 1/N Expansion; AdS-CFT Correspondence; Conformal Field Theory; Field Theories in Higher Dimensions

### Citation Formats

```
Giombi, Simone, Kirilin, Vladimir, and Perlmutter, Eric. Double-trace deformations of conformal correlations. United States: N. p., 2018.
Web. doi:10.1007/jhep02(2018)175.
```

```
Giombi, Simone, Kirilin, Vladimir, & Perlmutter, Eric. Double-trace deformations of conformal correlations. United States. doi:10.1007/jhep02(2018)175.
```

```
Giombi, Simone, Kirilin, Vladimir, and Perlmutter, Eric. Wed .
"Double-trace deformations of conformal correlations". United States. doi:10.1007/jhep02(2018)175. https://www.osti.gov/servlets/purl/1507423.
```

```
@article{osti_1507423,
```

title = {Double-trace deformations of conformal correlations},

author = {Giombi, Simone and Kirilin, Vladimir and Perlmutter, Eric},

abstractNote = {Large N conformal field theories often admit unitary renormalization group flows triggered by double-trace deformations. We compute the change in scalar four-point functions under double-trace flow, to leading order in 1/N. This has a simple dual in AdS, where the flow is implemented by a change of boundary conditions, and provides a physical interpretation of single-valued conformal partial waves. We extract the change in the conformal dimensions and three-point coefficients of infinite families of double-trace composite operators. Some of these quantities are found to be sign-definite under double-trace flow. As an application, we derive anomalous dimensions of spinning double-trace operators comprised of non-singlet constituents in the O(N) vector model.},

doi = {10.1007/jhep02(2018)175},

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

number = 2,

volume = 2018,

place = {United States},

year = {2018},

month = {2}

}