The black hole weak gravity conjecture with multiple charges
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Springer
Received: February 5, 2020 Accepted: May 10, 2020 Published: June 23, 2020
Callum R.T. Jones and Brian McPeak Leinweber Center for Theoretical Physics, Randall Laboratory of Physics, The University of Michigan, Ann Arbor, MI 48109-1040, U.S.A.
E-mail: [email protected], [email protected] Abstract: We study the effect of higher-derivative corrections on asymptotically flat, fourdimensional, dyonic black holes in low-energy models of gravity coupled to N U(1) gauge fields. For large extremal black holes, the leading O 1/Q2 correction to the extremality bound is calculated from the most general low-energy effective action containing operators with up to four derivatives. Motivated by the multi-charge generalization of the Weak Gravity Conjecture, we analyze the necessary kinematic conditions for an asymptotically large extremal black hole to decay into a multi-particle state of extremal black holes. In the large black hole regime, we show that the convex hull condition degenerates to the requirement that a certain quartic form constructed from the Wilson coefficients of the fourderivative effective operators, is everywhere positive. Using on-shell unitarity methods, we show that higher-derivative operators are renormalized at one-loop only if they generate local, on-shell matrix elements that are invariant tensors of the electromagnetic duality group U(N ). The one-loop logarithmic running of the four-derivative Wilson coefficients is calculated and shown to imply the positivity of the extremality form at some finite value of Q2 . This result generalizes an argument recently given by Charles [1], and shows that under the given assumptions the multi-charge Weak Gravity Conjecture is not a Swampland criterion. Keywords: Black Holes, Effective Field Theories ArXiv ePrint: 1908.10452
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)140
JHEP06(2020)140
The black hole weak gravity conjecture with multiple charges
Contents 1 1 4
2 Extremality shift 2.1 No correction from three-derivative operators 2.2 Four-derivative operators 2.2.1 Background 2.2.2 Corrections to the background 2.2.3 Maxwell corrections 2.2.4 Lagrangian corrections 2.3 Leading shift to extremality bound
5 6 7 7 8 8 9 9
3 Black hole decay and the Weak Gravity Conjecture 3.1 Examples 3.1.1 Black hole with two electric charges 3.1.2 Dyonic black hole 3.2 Unitarity and causality 3.2.1 Integrating out massive particles 3.2.2 Causality constraints
10 12 12 12 14 14 17
4 Renormalization of four-derivative operators 4.1 Non-renormalization and electromagnetic duality 4.2 RG flow and the multi-charge Weak Gravity Conjecture
17 18 23
5 Discussion
26
A EFT basis and on-shell matrix elements A.1 Three-derivative operators A.2 Four-derivative operators
27 30 31
B Corrections to the Maxwell equation
32
C Variations of four-derivative operators with respect to the metric
33
D Proof of convexity of the extremality surface
34
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JHEP06(2020)140
1 Introduction 1.1 Review of the Weak Gravity Co
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