## Double-trace flows and the swampland

## Abstract

We explore the idea that large *N*, non-supersymmetric conformal field theories with a parametrically large gap to higher spin single-trace operators may be obtained as infrared fixed points of relevant double-trace deformations of superconformal field theories. After recalling the AdS interpretation and some potential pathologies of such flows, we introduce a concrete example that appears to avoid them: the ABJM theory at finite *k*, deformed by ∫O ^{2}, where O is the superconformal primary in the stress-tensor multiplet. We address its relation to recent conjectures based on weak gravity bounds, and discuss the prospects for a wider class of similarly viable flows. Next, we proceed to analyze the spectrum and correlation functions of the putative IR CFT, to leading non-trivial order in 1/ *N*. This includes analytic computations of the change under double-trace flow of connected four-point functions of ABJM superconformal primaries; and of the IR anomalous dimensions of infinite classes of double-trace composite operators. These would be the first analytic results for anomalous dimensions of finite-spin composite operators in any large *N* CFT _{3} with an Einstein gravity dual.

- Authors:

- Princeton Univ., Princeton, NJ (United States). Dept. of Physics
- 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:
- 1507424

- Grant/Contract Number:
- FG02-91ER40671; SC0011632; PHY-1620542; 48865

- 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: 3; 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, and Perlmutter, Eric. Double-trace flows and the swampland. United States: N. p., 2018.
Web. doi:10.1007/jhep03(2018)026.
```

```
Giombi, Simone, & Perlmutter, Eric. Double-trace flows and the swampland. United States. doi:10.1007/jhep03(2018)026.
```

```
Giombi, Simone, and Perlmutter, Eric. Tue .
"Double-trace flows and the swampland". United States. doi:10.1007/jhep03(2018)026. https://www.osti.gov/servlets/purl/1507424.
```

```
@article{osti_1507424,
```

title = {Double-trace flows and the swampland},

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

abstractNote = {We explore the idea that large N, non-supersymmetric conformal field theories with a parametrically large gap to higher spin single-trace operators may be obtained as infrared fixed points of relevant double-trace deformations of superconformal field theories. After recalling the AdS interpretation and some potential pathologies of such flows, we introduce a concrete example that appears to avoid them: the ABJM theory at finite k, deformed by ∫O2, where O is the superconformal primary in the stress-tensor multiplet. We address its relation to recent conjectures based on weak gravity bounds, and discuss the prospects for a wider class of similarly viable flows. Next, we proceed to analyze the spectrum and correlation functions of the putative IR CFT, to leading non-trivial order in 1/N. This includes analytic computations of the change under double-trace flow of connected four-point functions of ABJM superconformal primaries; and of the IR anomalous dimensions of infinite classes of double-trace composite operators. These would be the first analytic results for anomalous dimensions of finite-spin composite operators in any large N CFT3 with an Einstein gravity dual.},

doi = {10.1007/jhep03(2018)026},

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

number = 3,

volume = 2018,

place = {United States},

year = {2018},

month = {3}

}