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Proof of the weak gravity conjecture from black hole entropy
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  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 01 October 2018

Proof of the weak gravity conjecture from black hole entropy

  • Clifford Cheung1,
  • Junyu Liu1 &
  • Grant N. Remmen2,3 

Journal of High Energy Physics volume 2018, Article number: 4 (2018) Cite this article

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A preprint version of the article is available at arXiv.

Abstract

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.

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Authors and Affiliations

  1. Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA, 91125, U.S.A.

    Clifford Cheung & Junyu Liu

  2. Center for Theoretical Physics and Department of Physics, University of California, Berkeley, CA, 94720, U.S.A.

    Grant N. Remmen

  3. Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, U.S.A.

    Grant N. Remmen

Authors
  1. Clifford Cheung
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  3. Grant N. Remmen
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Correspondence to Grant N. Remmen.

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ArXiv ePrint: 1801.08546

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Cheung, C., Liu, J. & Remmen, G.N. Proof of the weak gravity conjecture from black hole entropy. J. High Energ. Phys. 2018, 4 (2018). https://doi.org/10.1007/JHEP10(2018)004

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  • Received: 10 May 2018

  • Revised: 28 August 2018

  • Accepted: 11 September 2018

  • Published: 01 October 2018

  • DOI: https://doi.org/10.1007/JHEP10(2018)004

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Keywords

  • Black Holes
  • Effective Field Theories
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