本征态热化的相变：通过AGT对应实现的禁戒奇点与瞬子增殖
Phase transition from eigenstate thermalization: forbidden singularity and instanton proliferation via AGT correspondence
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中文总结 AI 辅助
本文利用AGT对应，将二维CFT中本征态热化的禁戒奇点与N=2超对称规范理论瞬子气体的相变关联，确定临界逸度对应禁戒奇点。
中文摘要 AI 辅助
在理论物理学中，寻找不同领域问题间的联系是实现突破性进展的重要途径，往往能揭示原本可能模糊的深层内涵。本文研究二维共形场论（2d CFT）中自关联函数的禁戒奇点现象——这是本征态热化的关键特征，证明其对应本征态语境下的相变。通过AGT对应建立明确联系，该对应将本征态自关联与描述N=2超对称（SUSY）规范理论瞬子气体的Nekrasov配分函数关联起来。通过取重轻极限的对应形式，瞬子气体呈现出两个相，分别由具有不同结构和热力学性质的类弦杨图构型主导，与禁闭相和解禁闭相极为相似。随着瞬子从一侧增殖，会发生类似李-杨（Lee-Yang）理论的相变。我们计算出临界逸度，发现其恰好对应禁戒奇点。
英文摘要
In theoretical physics, finding connections between problems that appear in distinct contexts is an important way to leapfrog progresses, often by illuminating deep aspects that may otherwise seem obscure. In this paper, we consider in 2d CFTs the phenomenon of forbidden singularities in auto-correlation functions -- a key signature of eigenstate thermalization. We show that they correspond to phase transitions in the context of eigenstates. The connection is made explicit by utilizing the AGT correspondence, which relates eigenstate auto-correlations to the Nekrasov partition functions describing an instanton gas of the $\mathcal{N}=2$ SUSY gauge theories. We show that by taking the counter-part of the heavy-light limit, two phases emerge for the instanton gas. They are dominated by configurations represented by string-like Young tableaux with distinct structures and thermodynamic properties, which bare resemblance to the confined and the deconfined phases. A phase transition occurs as instantons proliferate from one side, in a manner that mimics the Lee-Yang theory. We work out the critical fugacity and find it corresponding exactly to the forbidden singularity.
