AI 中文总结
研究量子引力中全局对称性是否因虫洞而破缺的问题，通过对α参数系综平均分析，发现广泛情形下对称点主导，其他破缺点贡献被抑制，如标准$\mathrm{U}(1)$佩切伊 - 奎因模型，解决了传统轴子质量问题。
AI 中文摘要
人们普遍认为，在量子引力的自洽理论中不存在全局对称性。引力瞬子或欧几里得虫洞为这一预期提供了一个突出机制，它们对欧几里得路径积分的贡献在有效作用量中产生局部对称性破缺算符，其耦合由α参数$\overrightarrow{\alpha}=(\alpha_1,\alpha_2,\cdots)$参数化。这些α参数的出现常被视为虫洞明确打破全局对称性的证据。本文认为这一结论为时过早。对称性的命运由这些α参数的系综平均决定。我们表明，在广泛情形下，这种平均可由对称点$\overrightarrow{\alpha}=0$主导，而其他对称性破缺临界点$\overrightarrow{\alpha}\neq0$的贡献通常被双指数因子$\exp(-e^{2S_{\rm ins}})$抑制，其中$S_{\rm ins}$是瞬子作用量。特别是，标准的$\mathrm{U}(1)$佩切伊 - 奎因模型属于此类，这意味着在虫洞诱导的有效理论中不会出现传统的轴子质量问题。我们的分析针对一般的$\mathrm{U}(1)$ $p$形式全局对称性进行阐述。
英文摘要
It is widely believed that global symmetries cannot exist in a consistent theory of quantum gravity. A prominent mechanism underlying this expectation is provided by gravitational instantons or Euclidean wormholes, whose contributions to the Euclidean path integral generates local symmetry-breaking operators in the effective action with couplings parametrized by the $α$-parameters $\overrightarrowα=(α_1^{},α_2^{},\cdots)$. The appearance of these $α$-parameters is often taken as evidence that wormholes explicitly break global symmetries. In this paper, we argue that this conclusion is premature. The fate of the symmetry is determined by the ensemble average over these $α$-parameters. We show that, under broad situations, this average can be sharply dominated by the symmetric point $\overrightarrowα=0$, while contributions from other symmetry-breaking critical points $\overrightarrowα\neq 0$ are typically suppressed by a doubly exponential factor $\exp(-e^{2S_{\rm ins}})$, where $S_{\rm ins}$ is the instanton action. In particular, standard $\mathrm{U}(1)^{}$ Peccei--Quinn models fall into this class, implying that the conventional axion quality problem does not arise in the wormhole-induced effective theory. Our analysis is formulated for general $\mathrm{U}(1)^{}$ $p$-form global symmetries.
Comments8 pages, 3 figures
