# 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:
- 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},

number = [4],

volume = [78],

place = {United States},

year = {2018},

month = {4}

}

*Citation information provided by*

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#### Figures / Tables:

Works referenced in this record:

##
ETHOS—an effective theory of structure formation: From dark particle physics to the matter distribution of the Universe

journal, June 2016

- Cyr-Racine, Francis-Yan; Sigurdson, Kris; Zavala, Jesús
- Physical Review D, Vol. 93, Issue 12

##
A note on gauge theories coupled to gravity

journal, September 2006

- Banks, Tom; Johnson, Matt; Shomer, Assaf
- Journal of High Energy Physics, Vol. 2006, Issue 09

##
Low-energy effective field theory for chromo-natural inflation

journal, February 2013

- Dimastrogiovanni, Emanuela; Fasiello, Matteo; Tolley, Andrew J.
- Journal of Cosmology and Astroparticle Physics, Vol. 2013, Issue 02

##
On the geometry of the string landscape and the swampland

journal, March 2007

- Ooguri, Hirosi; Vafa, Cumrun
- Nuclear Physics B, Vol. 766, Issue 1-3

##
A Chern-Simons pandemic

journal, July 2017

- Montero, Miguel; Uranga, Angel M.; Valenzuela, Irene
- Journal of High Energy Physics, Vol. 2017, Issue 7

##
Natural Inflation on a Steep Potential with Classical Non-Abelian Gauge Fields

journal, June 2012

- Adshead, Peter; Wyman, Mark
- Physical Review Letters, Vol. 108, Issue 26

##
The Weak Gravity Conjecture in three dimensions

journal, October 2016

- Montero, Miguel; Shiu, Gary; Soler, Pablo
- Journal of High Energy Physics, Vol. 2016, Issue 10

##
Large-field inflation with multiple axions and the weak gravity conjecture

journal, February 2016

- Junghans, Daniel
- Journal of High Energy Physics, Vol. 2016, Issue 2

##
Black hole bound on the number of species and quantum gravity at CERN LHC

journal, February 2008

- Dvali, Gia; Redi, Michele
- Physical Review D, Vol. 77, Issue 4

##
Constraints on axion inflation from the weak gravity conjecture

journal, September 2015

- Rudelius, Tom
- Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 09

##
Winding out of the Swamp: Evading the weak gravity conjecture with F -term winding inflation?

journal, September 2015

- Hebecker, Arthur; Mangat, Patrick; Rompineve, Fabrizio
- Physics Letters B, Vol. 748

##
A note on the WGC, effective field theory and clockwork within string theory

journal, February 2018

- Ibáñez, Luis E.; Montero, Miguel
- Journal of High Energy Physics, Vol. 2018, Issue 2

##
Natural inflation with pseudo Nambu-Goldstone bosons

journal, December 1990

- Freese, Katherine; Frieman, Joshua A.; Olinto, Angela V.
- Physical Review Letters, Vol. 65, Issue 26

##
Not even decoupling can save the minimal supersymmetric SU(5) model

journal, February 2002

- Murayama, Hitoshi; Pierce, Aaron
- Physical Review D, Vol. 65, Issue 5

##
Symmetries and strings in field theory and gravity

journal, April 2011

- Banks, Tom; Seiberg, Nathan
- Physical Review D, Vol. 83, Issue 8

##
Weak gravity conjecture and effective field theory

journal, January 2017

- Saraswat, Prashant
- Physical Review D, Vol. 95, Issue 2

##
The Weak Gravity Conjecture and the axionic black hole paradox

journal, September 2017

- Hebecker, Arthur; Soler, Pablo
- Journal of High Energy Physics, Vol. 2017, Issue 9

##
Charged black holes in string theory

journal, May 1991

- Garfinkle, David; Horowitz, Gary T.; Strominger, Andrew
- Physical Review D, Vol. 43, Issue 10

##
Fencing in the swampland: quantum gravity constraints on large field inflation

journal, October 2015

- Brown, Jon; Cottrell, William; Shiu, Gary
- Journal of High Energy Physics, Vol. 2015, Issue 10

##
A proof of the weak gravity conjecture

journal, October 2017

- Hod, Shahar
- International Journal of Modern Physics D, Vol. 26, Issue 12

##
*N* -flation

journal, August 2008

- Dimopoulos, S.; Kachru, S.; McGreevy, J.
- Journal of Cosmology and Astroparticle Physics, Vol. 2008, Issue 08

##
Higgsed Chromo-Natural Inflation

journal, December 2016

- Adshead, Peter; Martinec, Emil; Sfakianakis, Evangelos I.
- Journal of High Energy Physics, Vol. 2016, Issue 12

##
The string landscape, black holes and gravity as the weakest force

journal, June 2007

- Arkani-Hamed, Nima; Motl, Luboš; Nicolis, Alberto
- Journal of High Energy Physics, Vol. 2007, Issue 06

##
Black holes in higher dimensional space-times

journal, December 1986

- Myers, R. C.; Perry, M. J.
- Annals of Physics, Vol. 172, Issue 2

##
Evidence for dark matter interactions in cosmological precision data?

journal, February 2016

- Lesgourgues, Julien; Marques-Tavares, Gustavo; Schmaltz, Martin
- Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 02

##
Non-Gaussianities and chiral gravitational waves in natural steep inflation

journal, June 2012

- Anber, Mohamed M.; Sorbo, Lorenzo
- Physical Review D, Vol. 85, Issue 12

##
Flat monodromies and a Moduli Space Size Conjecture

journal, December 2017

- Hebecker, Arthur; Henkenjohann, Philipp; Witkowski, Lukas T.
- Journal of High Energy Physics, Vol. 2017, Issue 12

##
Evidence for a sublattice weak gravity conjecture

journal, August 2017

- Heidenreich, Ben; Reece, Matthew; Rudelius, Tom
- Journal of High Energy Physics, Vol. 2017, Issue 8

##
Transplanckian axions!?

journal, August 2015

- Montero, Miguel; Uranga, Angel M.; Valenzuela, Irene
- Journal of High Energy Physics, Vol. 2015, Issue 8

##
What is the magnetic Weak Gravity Conjecture for axions?: WGC for Axions

journal, March 2017

- Hebecker, Arthur; Henkenjohann, Philipp; Witkowski, Lukas T.
- Fortschritte der Physik, Vol. 65, Issue 3-4

##
Gauge-flation vs chromo-natural inflation

journal, October 2012

- Sheikh-Jabbari, M. M.
- Physics Letters B, Vol. 717, Issue 1-3

##
Sharpening the weak gravity conjecture with dimensional reduction

journal, February 2016

- Heidenreich, Ben; Reece, Matthew; Rudelius, Tom
- Journal of High Energy Physics, Vol. 2016, Issue 2

##
Wormholes, emergent gauge fields, and the weak gravity conjecture

journal, January 2016

- Harlow, Daniel
- Journal of High Energy Physics, Vol. 2016, Issue 1

##
Gauge-flation: Inflation from non-Abelian gauge fields

journal, June 2013

- Maleknejad, A.; Sheikh-Jabbari, M. M.
- Physics Letters B, Vol. 723, Issue 1-3

##
Planckian axions and the Weak Gravity Conjecture

journal, January 2016

- Bachlechner, Thomas C.; Long, Cody; McAllister, Liam
- Journal of High Energy Physics, Vol. 2016, Issue 1

##
Massless black holes and conifolds in string theory

journal, September 1995

- Strominger, Andrew
- Nuclear Physics B, Vol. 451, Issue 1-2

##
Gaugid inflation

journal, November 2017

- Piazza, Federico; Pirtskhalava, David; Rattazzi, Riccardo
- Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 11

##
Perturbations in Chromo-Natural Inflation

journal, September 2013

- Adshead, Peter; Martinec, Emil; Wyman, Mark
- Journal of High Energy Physics, Vol. 2013, Issue 9

##
Super-Planckian spatial field variations and quantum gravity

journal, January 2017

- Klaewer, Daniel; Palti, Eran
- Journal of High Energy Physics, Vol. 2017, Issue 1

##
Proton decay at M pl and the scale of SUSY-breaking

journal, February 2014

- Dine, Michael; Draper, Patrick; Shepherd, William
- Journal of High Energy Physics, Vol. 2014, Issue 2

##
Interacting dark sector and precision cosmology

journal, January 2018

- Buen-Abad, Manuel A.; Schmaltz, Martin; Lesgourgues, Julien
- Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 01

##
Gauge-flation trajectories in chromo-natural inflation

journal, August 2012

- Adshead, Peter; Wyman, Mark
- Physical Review D, Vol. 86, Issue 4

##
Antigravitating black hole solitons with scalar hair in N=4 supergravity

journal, November 1982

- Gibbons, G. W.
- Nuclear Physics B, Vol. 207, Issue 2

##
The weak gravity conjecture and scalar fields

journal, August 2017

- Palti, Eran
- Journal of High Energy Physics, Vol. 2017, Issue 8

##
Discrete gauge symmetry anomalies

journal, May 1991

- Ibáñez, L. E.; Ross, G. G.
- Physics Letters B, Vol. 260, Issue 3-4

##
The swampland conjecture and F-term axion monodromy inflation

journal, July 2017

- Blumenhagen, Ralph; Valenzuela, Irene; Wolf, Florian
- Journal of High Energy Physics, Vol. 2017, Issue 7

##
Torsion-balance tests of the weak equivalence principle

journal, August 2012

- Wagner, T. A.; Schlamminger, S.; Gundlach, J. H.
- Classical and Quantum Gravity, Vol. 29, Issue 18

##
Backreaction issues in axion monodromy and Minkowski 4-forms

journal, June 2017

- Valenzuela, Irene
- Journal of High Energy Physics, Vol. 2017, Issue 6

##
Transplanckian censorship and global cosmic strings

journal, April 2017

- Dolan, Matthew J.; Draper, Patrick; Kozaczuk, Jonathan
- Journal of High Energy Physics, Vol. 2017, Issue 4

##
Axion experiments to algebraic geometry: Testing quantum gravity via the Weak Gravity Conjecture

journal, October 2016

- Heidenreich, Ben; Reece, Matthew; Rudelius, Tom
- International Journal of Modern Physics D, Vol. 25, Issue 12

##
Non-Abelian dark matter and dark radiation

journal, July 2015

- Buen-Abad, Manuel A.; Marques-Tavares, Gustavo; Schmaltz, Martin
- Physical Review D, Vol. 92, Issue 2

##
Gauge fields and inflation

journal, July 2013

- Maleknejad, A.; Sheikh-Jabbari, M. M.; Soda, J.
- Physics Reports, Vol. 528, Issue 4

##
Weak Gravity Conjecture and Black Holes in $N = 2$ Supergravity

conference, October 2017

- Shiu, Gary; Cottrell, William; Soler, Pablo
- Proceedings of Corfu Summer Institute 2016 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2016)

##
Black holes and membranes in higher-dimensional theories with dilaton fields

journal, March 1988

- Gibbons, G. W.; Maeda, Kei-ichi
- Nuclear Physics B, Vol. 298, Issue 4

##
A phenomenological comparison of conventional and supersymmetric guts

journal, July 1982

- Ellis, John; Nanopoulos, D. V.; Rudaz, Serge
- Nuclear Physics B, Vol. 202, Issue 1

##
Primordial gravitational waves from axion-gauge fields dynamics

journal, January 2017

- Dimastrogiovanni, Emanuela; Fasiello, Matteo; Fujita, Tomohiro
- Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 01

##
Evaporation of microscopic black holes in string theory and the bound on species

journal, April 2010

- Dvali, G.; Lüst, D.
- Fortschritte der Physik, Vol. 58, Issue 6

##
Wandering in the Lyman-alpha forest: a study of dark matter-dark radiation interactions

journal, September 2017

- Krall, Rebecca; Cyr-Racine, Francis-Yan; Dvorkin, Cora
- Journal of Cosmology and Astroparticle Physics, Vol. 2017, Issue 09

##
Black holes and large N species solution to the hierarchy problem

journal, April 2010

- Dvali, G.
- Fortschritte der Physik, Vol. 58, Issue 6

##
Supersymmetry at ordinary energies. Masses and conservation laws

journal, July 1982

- Weinberg, Steven
- Physical Review D, Vol. 26, Issue 1

##
Partially acoustic dark matter, interacting dark radiation, and large scale structure

journal, December 2016

- Chacko, Zackaria; Cui, Yanou; Hong, Sungwoo
- Journal of High Energy Physics, Vol. 2016, Issue 12

##
Backreacted axion field ranges in string theory

journal, August 2016

- Baume, Florent; Palti, Eran
- Journal of High Energy Physics, Vol. 2016, Issue 8

##
Running of the gravitational constant

journal, May 2012

- Anber, Mohamed M.; Donoghue, John F.
- Physical Review D, Vol. 85, Issue 10

##
Gauge fields and inflation: Chiral gravitational waves, fluctuations, and the Lyth bound

journal, July 2013

- Adshead, Peter; Martinec, Emil; Wyman, Mark
- Physical Review D, Vol. 88, Issue 2

##
Naturalness and the Weak Gravity Conjecture

journal, July 2014

- Cheung, Clifford; Remmen, Grant N.
- Physical Review Letters, Vol. 113, Issue 5

##
Non-Abelian gauge preheating

journal, December 2017

- Adshead, Peter; Giblin, John T.; Weiner, Zachary J.
- Physical Review D, Vol. 96, Issue 12

##
Evidence for an electrifying violation of cosmic censorship

journal, September 2016

- Horowitz, Gary T.; Santos, Jorge E.; Way, Benson
- Classical and Quantum Gravity, Vol. 33, Issue 19

##
Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti–de Sitter Space

journal, May 2017

- Crisford, Toby; Santos, Jorge E.
- Physical Review Letters, Vol. 118, Issue 18

##
Does the detection of primordial gravitational waves exclude low energy inflation?

journal, March 2018

- Fujita, Tomohiro; Namba, Ryo; Tada, Yuichiro
- Physics Letters B, Vol. 778

Works referencing / citing this record:

##
Pole N-flation

journal, February 2019

- Dias, Mafalda; Frazer, Jonathan; Retolaza, Ander
- Journal of High Energy Physics, Vol. 2019, Issue 2

##
Racing through the swampland: de Sitter uplift vs. weak gravity

journal, September 2018

- Moritz, Jakob; Van Riet, Thomas
- Journal of High Energy Physics, Vol. 2018, Issue 9

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*