arXiv 2002.024562020-02hep-thhep-ph

利用弱引力实现沼泽地全球对称性猜想

Towards a Swampland Global Symmetry Conjecture using Weak Gravity

Tristan Daus, Arthur Hebecker, Sascha Leonhardt, John March-Russell

备注：: 23 pages, 2 figures; v3: Appendix on new Euclidean wormhole solution with charged particle added. Extended discussion of other subtopics
DOI：: 10.1016/j.nuclphysb.2020.115167

摘要：

人们普遍认为，精确的全局对称性与量子引力不一致，这在一定程度上得到了证实。于是，人们期望近似的全局对称性可以被量子引力或沼泽地论点定量地约束。我们为一类重要的全局对称性提供了这样一个界：这些全局对称性是由规范的$U(1)$产生的，其矢量通过希格斯辛和轴子而变得巨大。后者必然与瞬子耦合，并且它们的作用可以被限制，根据理论的截止，使用公理弱引力猜想的电和磁版本。其结果是，瞬子诱导的对称性破缺算子的抑制因子不小于$\exp(-M_{\rm P}^2/Λ^2)$，其中$Λ$是一个截止的4d有效理论。我们提供了一个一般性的论点，并澄清了$Λ$的含义。简单的4d和5d模型被用来说明这一点，我们记得这是用膜瞬子进行弦紧化的标准方式。我们的约束的关系，可以从虫洞或引力瞬子和黑洞的影响，在有限的温度下的动机的界限进行了讨论，我们提出了一个推广的Giddings-Strominger虫洞解决方案的情况下，规范导出的$U(1)$全球对称性。最后，我们讨论了我们的论点的潜在漏洞。

英文摘要：

It is widely believed and in part established that exact global symmetries are inconsistent with quantum gravity. One then expects that approximate global symmetries can be quantitatively constrained by quantum gravity or swampland arguments. We provide such a bound for an important class of global symmetries: Those arising from a gauged $U(1)$ with the vector made massive via Higgsing with an axion. The latter necessarily couples to instantons, and their action can be constrained, using both the electric and magnetic version of the axionic weak gravity conjecture, in terms of the cutoff of the theory. As a result, instanton-induced symmetry breaking operators with a suppression factor not smaller than $\exp(-M_{\rm P}^2/Λ^2)$ are present, where $Λ$ is a cutoff of the 4d effective theory. We provide a general argument and clarify the meaning of $Λ$. Simple 4d and 5d models are presented to illustrate this, and we recall that this is the standard way in which things work out in string compactifications with brane instantons. The relation of our constraint to bounds that can be derived from wormholes or gravitational instantons and to those motivated by black-hole effects at finite temperature are discussed, and we present a generalization of the Giddings-Strominger wormhole solution to the case of a gauge-derived $U(1)$ global symmetry. Finally, we discuss potential loopholes to our arguments.

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