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Proof of the Weak Gravity Conjecture from Black Hole Entropy

Cheung, Clifford and Liu, Junyu and Remmen, Grant N. (2018) Proof of the Weak Gravity Conjecture from Black Hole Entropy. Journal of High Energy Physics, 2018 (10). Art. No. 4. ISSN 1126-6708. doi:10.1007/JHEP10(2018)004.

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We prove that higher-dimension operators contribute positively to the entropy of a thermodynamically stable black hole at fixed mass and charge. Our results apply whenever the dominant corrections originate at tree level from quantum field theoretic dynamics. More generally, positivity of the entropy shift is equivalent to a certain inequality relating the free energies of black holes. These entropy inequalities mandate new positivity bounds on the coefficients of higher-dimension operators. One of these conditions implies that the charge-to-mass ratio of an extremal black hole asymptotes to unity from above for increasing mass. Consequently, large extremal black holes are unstable to decay to smaller extremal black holes and the weak gravity conjecture is automatically satisfied. Our findings generalize to arbitrary spacetime dimension and to the case of multiple gauge fields. The assumptions of this proof are valid across a range of scenarios, including string theory constructions with a dilaton stabilized below the string scale.

Item Type:Article
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URLURL TypeDescription Paper
Liu, Junyu0000-0003-1669-8039
Remmen, Grant N.0000-0001-6569-8866
Additional Information:© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: May 10, 2018. Revised: August 28, 2018. Accepted: September 11, 2018. Published: October 1, 2018. We thank Nima Arkani-Hamed, Raphael Bousso, Sean Carroll, William Cottrell, Daniel Harlow, Tom Hartman, Yasunori Nomura, Hirosi Ooguri, Matthew Reece, Prashant Saraswat, Gary Shiu, Leo Stein, and Aron Wall for helpful discussions. C.C. and J.L. are supported by a Sloan Research Fellowship and DOE Early Career Award under grant no. DE-SC0010255. G.N.R. is supported by the Miller Institute for Basic Research in Science at the University of California, Berkeley.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0010255
Miller Institute for Basic Research in ScienceUNSPECIFIED
Subject Keywords:Black Holes; Effective Field Theories
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Issue or Number:10
Record Number:CaltechAUTHORS:20180228-094915466
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84998
Deposited By: Joy Painter
Deposited On:28 Feb 2018 18:11
Last Modified:15 Nov 2021 20:24

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