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arXiv 1908.10452hep-th
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多重荷黑洞弱引力猜想

The Black Hole Weak Gravity Conjecture with Multiple Charges

Callum R. T. Jones, Brian McPeak

摘要:

在耦合到$N$ $U(1)$规范场的低能引力模型中,研究了高阶导数修正对渐近平坦的四维非旋转双子黑洞的影响.对于大的极值黑洞,领先的$\mathcal{O}\left(1/Q^2\right)$校正的极值界计算从最一般的低能量有效的行动包含运营商多达四个衍生物。受弱引力猜想的多电荷推广的启发,我们分析了渐近大极值黑洞衰变为有限电荷极值黑洞的多粒子态的必要运动学条件.在大黑洞制度,我们表明,凸壳条件退化的要求,一定的四次形式,从威尔逊系数的四阶导数有效运营商,处处是积极的。使用上壳么正性方法,我们表明,高导数算子重整化在一个循环,只有当他们产生本地,上壳矩阵元素是不变的张量的电磁对偶群$U(N)$。计算了四阶导数Wilson系数的单圈对数运行,并表明在$Q^2$的某个有限值处极值形式为正。这一结果推广了Charles最近给出的一个论点,并表明在给定的假设下,多电荷弱引力猜想不是沼泽地判据。

英文摘要:

We study the effect of higher-derivative corrections on asymptotically flat, four-dimensional, non-rotating dyonic black holes in low-energy models of gravity coupled to $N$ $U(1)$ gauge fields. For large extremal black holes, the leading $\mathcal{O}\left(1/Q^2\right)$ 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 finite charge 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 four-derivative 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 a recently given argument by Charles, and shows that under the given assumptions the multi-charge Weak Gravity Conjecture is not a Swampland criterion.

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