The black hole weak gravity conjecture with multiple charges

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/Q 2 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 Q 2. 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.

Thermodynamics of 4D dilatonic black holes and the weak gravity conjecture

“…References [10,11] have recently shown that one-loop contributions to the Wilson coefficients generically lead to the weak form of the WGC being satisfied in the deep IR. It would be interesting to investigate this argument with the exponential coupling of the dilaton considered here.…”

“…where M represents the black hole's mass and Q e , Q m , and Q ϕ represent its electric, magnetic, and scalar charges, respectively. The weak version of the WGC has been demonstrated, under some assumptions, 1 in Einstein-Maxwell theory [8][9][10][11]. See also [12][13][14][15][16][17][18][19][20][21] for more discussions of the conjecture.…”

Higher-derivative corrections to entropy and the weak gravity conjecture in Anti-de Sitter space

“…The statement that black holes can always decay through these higher-derivative corrections is sometimes called the "Black Hole Weak Gravity Conjecture." This idea has inspired a large amount of work [5][6][7][8][9][10][11] on bounding the EFT coefficients, thereby proving the conjecture. While no existing proof is completely general, the work so far covers a large number of possibilities and assumptions.…”

The Entropy Shift and Extremality Shift at Zero Temperature

“…It is interesting that d 0 , the combination which is related to the WGC, enters the T = 0 entropy shift with the opposite sign as the constant m entropy shift of [19]. Furthermore, consider that for magnetic black holes, ∆m ∼ −(d 0 + 2d 6 ) [9] (see appendix also). Therefore enforcing the WGC (or alternatively, the positivity of the fixed-mass entropy shift) for all charged black holes in 4d tells us…”

“…Recently there has been a lot of progress on understanding if the required inequality does indeed hold using diverse arguments including consistency of the S-matrix [4][5][6][7], RG running [8][9][10], modular invariance [11], the c-theorem [12], and investigating various specific examples [13][14][15] and consequences [16][17][18]. A particularly intriguing argument [19] is that the combination of EFT coefficients which appears in the WGC calculation of [2] is (−1) times the same combination that appears in the shift to the black hole entropy at extremality.…”