发表机构
The University of Tokyo; Yukawa Institute for Theoretical Physics, Kyoto University; North Carolina State University（东京大学; 京都大学汤川理论物理研究所; 北卡罗来纳州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出$\u2102P^{N-1}$模型的双耦合推广形式，通过大$N$求解确定自对偶理论真空结构，引入边界顶针解决鞍点能量佯谬，恢复强耦合理论大$N$展开的有效性。
AI 中文摘要
我们提出了$\u2102P^{N-1}$模型的一种双耦合推广形式，它可在自对偶（$\u03b5=0$）理论与物理（$\u03b5=g$）理论之间连续插值，是一种实用的非微扰工具。当$\u03b5\u2260g$时，该模型存在手征不平衡，可被视为一种实拓扑形变（虚$\theta$）。我们证明，一阶与二阶表述之间的严格量子精确等价，需要一个由玻色手征反常源起的拓扑抵消项。在大$N$下求解该形变理论得到两个主要结果。第一，我们解析确定了自对偶理论的非微扰真空结构，即一种带有动力学产生的场强凝聚体的自对偶真空。第二，我们解决了一个基本佯谬：满足$(θ+2πn)\u223cO(N)$（$n$为分支数）的鞍点会虚假地给出比物理基态更低的能量密度。由于有效作用量在$F=0$处存在本性奇点，我们表明必须推广莱夫谢茨顶针（Lefschetz thimble）分析以纳入边界顶针。边界斯托克斯现象使这些有问题的鞍点在拓扑上失去活性，完全恢复了强耦合理论大$N$展开的有效性。
英文摘要
We introduce a two-coupling generalization of $\mathbb{C}P^{N-1}$ model that continuously interpolates between the self-dual ($ε=0$) and the physical ($ε=g$) theories as a useful nonperturbative tool. At $ε\neq g$, this model possesses a chiral imbalance, which may be viewed as a real topological deformation (imaginary-$θ$). We demonstrate that exact quantum equivalence between first- and second-order formulations strictly requires a topological counterterm sourced by a bosonic chiral anomaly. Solving this deformed theory at large $N$ yields two primary results. First, we analytically determine the nonperturbative vacuum structure of the self-dual theory, a self-dual vacuum with a dynamically generated field-strength condensate. Second, we resolve a fundamental paradox where saddles with $(θ+ 2πn) \sim O(N)$ ($n$ is branch number) spuriously yield lower energy densities than the physical ground state. Because the effective action possesses an essential singularity at $F=0$, we show that the Lefschetz thimble analysis must be generalized to include boundary thimbles. A boundary Stokes phenomenon renders the problematic saddles topologically inactive, fully restoring the validity of the large-$N$ expansion for strongly coupled theories.
Comments64 pages, 10 figures
