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arXiv 1503.07853hep-th
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普朗克轴子与弱引力猜想

Planckian Axions and the Weak Gravity Conjecture

Thomas C. Bachlechner, Cody Long, Liam McAllister

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20 pages, 2 figures
发表信息：
JHEP 1601 (2016) 091
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摘要：

最近的几项工作声称，弱引力猜想（WGC）排除了轴子场的超普朗克位移，因此在没有单值性的情况下排除了大场轴子暴胀。我们认为，在理论与$N\gg1$轴子，超普朗克轴子直径$\cal{D}$很容易被允许的WGC。我们澄清的动力学矩阵$K$ --明确定义的形式在闵可夫斯基减少基础--和轴子的基本域的直径之间的非平凡的关系，强调在一般情况下，直径是不完全由本征值$f_1^2 \le ... \le f_N^2$的$K$：本征向量的方向相对于瞬子所施加的标识必须纳入。特别地，即使要强加条件$f_N<M_{pl}$，这也将既不意味着${\cal D}<M_{pl}$也不意味着${\cal D}<\sqrt{N}M_{pl}$。然后，我们估计满足WGC的瞬子的行动。主导瞬子作用量由$S \ge {\cal S} M_{pl}/f_N$限定，${\cal S}$是一个固定常数，但在普适极限$S\gtrsim {\cal S} \sqrt{N}M_{pl}/f_N$内。因此，具有$f_N>M_{pl}$并不直接意味着存在对电势的未抑制的高次谐波贡献。最后，我们认为，在有效的轴子引力理论中，零形式的WGC可以满足引力瞬子，使潜在的贡献可以忽略不计。

英文摘要：

Several recent works have claimed that the Weak Gravity Conjecture (WGC) excludes super-Planckian displacements of axion fields, and hence large-field axion inflation, in the absence of monodromy. We argue that in theories with $N\gg1$ axions, super-Planckian axion diameters $\cal{D}$ are readily allowed by the WGC. We clarify the nontrivial relationship between the kinetic matrix $K$ --- unambiguously defined by its form in a Minkowski-reduced basis --- and the diameter of the axion fundamental domain, emphasizing that in general the diameter is not solely determined by the eigenvalues $f_1^2 \le ... \le f_N^2$ of $K$: the orientations of the eigenvectors with respect to the identifications imposed by instantons must be incorporated. In particular, even if one were to impose the condition $f_N<M_{pl}$, this would imply neither ${\cal D}<M_{pl}$ nor ${\cal D}<\sqrt{N}M_{pl}$. We then estimate the actions of instantons that fulfill the WGC. The leading instanton action is bounded from below by $S \ge {\cal S} M_{pl}/f_N$, with ${\cal S}$ a fixed constant, but in the universal limit $S\gtrsim {\cal S} \sqrt{N}M_{pl}/f_N$. Thus, having $f_N>M_{pl}$ does not immediately imply the existence of unsuppressed higher harmonic contributions to the potential. Finally, we argue that in effective axion-gravity theories, the zero-form version of the WGC can be satisfied by gravitational instantons that make negligible contributions to the potential.

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