量子相变与复苏：三维$\mathcal{N}=4$ SQED的经验教训
Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
摘要：
研究了具有相变的量子场论的复苏结构，揭示了复苏和相变之间的关系。特别是，我们专注于三维$\mathcal{N}=4$超对称量子电动力学（SQED）与多个超多重态，其中二阶量子相变最近已被提出的大味极限。我们提供的解释的相变从莱夫谢茨顶针和复苏的观点。为此，我们研究了由超对称局部化得到的配分函数的Lefschetz顶针结构和大味展开的性质。我们表明，二阶相变被理解为一种现象，其中斯托克斯和反斯托克斯现象同时发生。相变的顺序取决于鞍在临界点的碰撞方式。此外，由于超对称性，相变伴随着无限多的Stokes现象。这些特征被适当地映射到Borel平面结构中，正如复苏理论所期望的那样。鉴于SQED的教训，我们提供了一个更一般的讨论之间的关系复苏和相变。特别是，我们展示了如何从Borel重混技术的相变的信息解码。
英文摘要：
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 been recently 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 anti-Stokes phenomenon occurs 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 the 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.
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