# The Weak Gravity Conjecture and emergence from an ultraviolet cutoff

## Abstract

We study ultraviolet cutoffs associated with the Weak Gravity Conjecture (WGC) and Sublattice Weak Gravity Conjecture (sLWGC). There is a magnetic WGC cutoff at the energy scale eG$$ \mathbb -1/2\atop{N} $$ with an associated sLWGC tower of charged particles. A more fundamental cutoff is the scale at which gravity becomes strong and field theory breaks down entirely. By clarifying the nature of the sLWGC for non-abelian gauge groups we derive a parametric upper bound on this strong gravity scale for arbitrary gauge theories. Intriguingly, we show that in theories approximately saturating the sLWGC, the scales at which loop corrections from the tower of charged particles to the gauge boson and graviton propagators become important are parametrically identical. This suggests a picture in which gauge fields emerge from the quantum gravity scale by integrating out a tower of charged matter fields. We derive a converse statement: if a gauge theory becomes strongly coupled at or below the quantum gravity scale, the WGC follows. We sketch some phenomenological consequences of the UV cutoffs we derive.

- Authors:

- Perimeter Inst. for Theoretical Physics, Waterloo, (Canada)
- Harvard Univ., Cambridge, MA (United States)
- Inst. for Advanced Study, Princeton, NJ (United States)

- Publication Date:

- Research Org.:
- Harvard Univ., Cambridge, MA (United States)

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

- OSTI Identifier:
- 1510007

- Grant/Contract Number:
- SC0013607

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- European Physical Journal. C, Particles and Fields

- Additional Journal Information:
- Journal Volume: 78; Journal Issue: 4; Journal ID: ISSN 1434-6044

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Heidenreich, Ben, Reece, Matthew, and Rudelius, Tom.
```*The Weak Gravity Conjecture and emergence from an ultraviolet cutoff*. United States: N. p., 2018.
Web. doi:10.1140/epjc/s10052-018-5811-3.

```
Heidenreich, Ben, Reece, Matthew, & Rudelius, Tom.
```*The Weak Gravity Conjecture and emergence from an ultraviolet cutoff*. United States. doi:10.1140/epjc/s10052-018-5811-3.

```
Heidenreich, Ben, Reece, Matthew, and Rudelius, Tom. Thu .
"The Weak Gravity Conjecture and emergence from an ultraviolet cutoff". United States. doi:10.1140/epjc/s10052-018-5811-3. https://www.osti.gov/servlets/purl/1510007.
```

```
@article{osti_1510007,
```

title = {The Weak Gravity Conjecture and emergence from an ultraviolet cutoff},

author = {Heidenreich, Ben and Reece, Matthew and Rudelius, Tom},

abstractNote = {We study ultraviolet cutoffs associated with the Weak Gravity Conjecture (WGC) and Sublattice Weak Gravity Conjecture (sLWGC). There is a magnetic WGC cutoff at the energy scale eG$ \mathbb -1/2\atop{N} $ with an associated sLWGC tower of charged particles. A more fundamental cutoff is the scale at which gravity becomes strong and field theory breaks down entirely. By clarifying the nature of the sLWGC for non-abelian gauge groups we derive a parametric upper bound on this strong gravity scale for arbitrary gauge theories. Intriguingly, we show that in theories approximately saturating the sLWGC, the scales at which loop corrections from the tower of charged particles to the gauge boson and graviton propagators become important are parametrically identical. This suggests a picture in which gauge fields emerge from the quantum gravity scale by integrating out a tower of charged matter fields. We derive a converse statement: if a gauge theory becomes strongly coupled at or below the quantum gravity scale, the WGC follows. We sketch some phenomenological consequences of the UV cutoffs we derive.},

doi = {10.1140/epjc/s10052-018-5811-3},

journal = {European Physical Journal. C, Particles and Fields},

issn = {1434-6044},

number = 4,

volume = 78,

place = {United States},

year = {2018},

month = {4}

}