We study a resurgence structure of a quantum field theory with a phase transition to uncover relations between resurgence and phase transitions. In particular, we focus on three-dimensional $\mathcal{N}=4$ supersymmetric quantum electrodynamics (SQED) with multiple hypermultiplets, where a second-order quantum phase transition has recently been proposed in the large-flavor limit. We provide interpretations of the phase transition from the viewpoints of Lefschetz thimbles and resurgence. For this purpose, we study the Lefschetz thimble structure and properties of the large-flavor expansion for the partition function obtained by the supersymmetric localization. We show that the second-order phase transition is understood as a phenomenon where a Stokes and an anti-Stokes phenomenon occur simultaneously. The order of the phase transition is determined by how saddles collide at the critical point. In addition, the phase transition accompanies an infinite number of Stokes phenomena due to the supersymmetry. These features are appropriately mapped to the Borel plane structures as the resurgence theory expects. Given the lessons from SQED, we provide a more general discussion on the relationship between the resurgence and phase transitions. In particular, we show how the information on the phase transition is decoded from the Borel resummation technique.

中文翻译：

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量子相变与复苏：三维 $\mathcal{N}=4$ 超对称量子电动力学的教训

我们研究了具有相变的量子场论的回潮结构，以揭示回潮和相变之间的关系。特别是，我们专注于具有多个超多重态的三维 $\mathcal{N}=4$ 超对称量子电动力学（SQED），其中最近在大风味极限中提出了二阶量子相变。我们从 Lefschetz 顶针和复兴的角度提供了对相变的解释。为此，我们研究了超对称定位得到的配分函数的Lefschetz顶针结构和大风味展开的性质。我们表明，二阶相变被理解为斯托克斯和反斯托克斯现象同时发生的现象。相变的顺序取决于鞍座在临界点的碰撞方式。此外，由于超对称性，相变伴随着无数的斯托克斯现象。正如复兴理论所期望的那样，这些特征被适当地映射到 Borel 平面结构。鉴于 SQED 的经验教训，我们对复苏和相变之间的关系进行了更一般的讨论。特别是，我们展示了如何从 Borel 恢复技术中解码相变信息。我们对复苏和阶段转变之间的关系进行了更一般的讨论。特别是，我们展示了如何从 Borel 恢复技术中解码相变信息。我们对复苏和阶段转变之间的关系进行了更一般的讨论。特别是，我们展示了如何从 Borel 恢复技术中解码相变信息。