Planckian axions and the Weak Gravity Conjecture
Planckian axions and the Weak Gravity Conjecture
复制标题
普朗克轴子和弱引力猜想
DOI：
10.1007/jhep01(2016)091
复制
发表时间：
2015
影响因子：
5.4
通讯作者：
L. McAllister
中科院分区：
文献类型：
--
作者：
Thomas C. Bachlechner;Cody Long;L. McAllister
**摘要**
近期的一些研究工作[1 - 3]声称，在没有单值性的情况下，弱引力猜想（WGC）排除了轴子场的超普朗克位移，从而也排除了大场轴子暴胀。我们认为，在具有\(N\gg1\)个轴子的理论中，弱引力猜想很容易允许超普朗克轴子直径\(\mathcal{D}\)。我们阐明了动理学矩阵\(K\)（由其在闵可夫斯基约化基下的形式明确界定）与轴子基本域直径之间的非平凡关系，强调一般来说直径并非仅仅由\(K\)的特征值\(f_1^2\leq\cdots\leq f_N^2\)决定：必须考虑本征向量相对于瞬子所施加的等同关系的取向。特别地，即使施加条件\(f_N<M_{pl}\)，这既不意味着\(\mathcal{D}<M_{pl}\)，也不意味着\(\mathcal{D}<\sqrt{N}M_{pl}\)。然后我们估计了满足弱引力猜想的瞬子的作用量。主导瞬子作用量从下方被界定为\(S\geq\mathcal{S}M_{pl}/f_N\)，其中\(\mathcal{S}\)是一个固定常数，但在普遍极限下\(S\gtrsim\mathcal{S}\sqrt{N}M_{pl}/f_N\)。因此，\(f_N>M_{pl}\)并不立即意味着势中存在未被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，零形式的弱引力猜想可以通过对势贡献可忽略的引力瞬子来满足。
A bstractSeveral recent works [1-3] 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 ≫ 1 axions, super-Planckian axion diameters D$$ \mathcal{D} $$ are readily allowed by the WGC. We clarify the non-trivial 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 f12 ≤ ⋅ ⋅ ⋅ ≤ fN2 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 fN< Mpl, this would imply neither D$$ \mathcal{D} $$< Mpl nor D$$ \mathcal{D} $$<NMpl$$ \sqrt{N}{M}_{\mathrm{pl}} $$. We then estimate the actions of instantons that fulfill the WGC. The leading instanton action is bounded from below by S≥SMpl/fN$$ S\ge \mathcal{S}\;{M}_{\mathrm{pl}}/{f}_N $$, with S$$ \mathcal{S} $$ a fixed constant, but in the universal limit S≳SNMpl/fN$$ S\gtrsim \mathcal{S}\sqrt{N}\ {M}_{\mathrm{pl}}/{f}_N $$. Thus, having fN> Mpl 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.