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arXiv 1504.03566hep-th
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多重轴子的大场暴胀与弱引力猜想

Large-Field Inflation with Multiple Axions and the Weak Gravity Conjecture

Daniel Junghans

备注：
30+8 pages, 13 figures, 1 table. v2: several remarks and references added, version to appear in JHEP
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摘要：

本文讨论了弱引力猜想（WGC）对含有大量轴子$N$的大场暴胀一般模型的意义。我们首先表明，从自下而上的角度来看，这样的模型承认各种不同的制度的有效轴子衰变常数的增强，这取决于对齐的数量和瞬子项的数量，有助于标量势。这包括相对于$N$的无增强、幂律增强和指数增强的机制。作为特例，我们恢复了$N$ -flation的毕达哥拉斯增强，Bachlechner，Long和McAllister导出的$N$和$N^{3/2}$增强以及Choi，Kim和Yun的指数增强。然后，我们从与量子引力的一致性要求出发，分析了这些模型受到哪些自上而下的约束。特别是，WGC似乎意味着，有效的轴子衰变常数的增强必须不增长参数与$N$为$N \gg 1$。另一方面，最近的工作提出，在某些情况下，轴子可能会违反这个界限。我们的一般表达式的增强允许我们将这种可能性转化为一个条件的瞬子耦合到轴子的数量。我们认为，在大的$N$，与量子引力一致的模型必须要么允许超普朗克场漂移，要么有一个巨大的，甚至可能是指数级大，在标量势占主导地位的瞬子项的数量。

英文摘要：

In this note, we discuss the implications of the weak gravity conjecture (WGC) for general models of large-field inflation with a large number of axions $N$. We first show that, from the bottom-up perspective, such models admit a variety of different regimes for the enhancement of the effective axion decay constant, depending on the amount of alignment and the number of instanton terms that contribute to the scalar potential. This includes regimes of no enhancement, power-law enhancement and exponential enhancement with respect to $N$. As special cases, we recover the Pythagorean enhancement of $N$-flation, the $N$ and $N^{3/2}$ enhancements derived by Bachlechner, Long and McAllister and the exponential enhancement by Choi, Kim and Yun. We then analyze which top-down constraints are put on such models from the requirement of consistency with quantum gravity. In particular, the WGC appears to imply that the enhancement of the effective axion decay constant must not grow parametrically with $N$ for $N \gg 1$. On the other hand, recent works proposed that axions might be able to violate this bound under certain circumstances. Our general expression for the enhancement allows us to translate this possibility into a condition on the number of instantons that couple to the axions. We argue that, at large $N$, models consistent with quantum gravity must either allow super-Planckian field excursions or have an enormous, possibly even exponentially large, number of dominant instanton terms in the scalar potential.

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