AI 中文总结
研究由相关热算子变形置于德西特时空的二维伊辛模型，通过费米子化精确求解，计算宇宙学关联函数并与共形微扰理论比较，分析自旋和无序算子两点函数，展示非微扰重整化晚期微扰病态，提供量子场论动力学可解实验室。
AI 中文摘要
我们研究了由相关热算子变形并置于德西特（dS）时空的二维伊辛模型。尽管其原始形式存在强相互作用，但由于费米子化该理论可精确求解。我们计算了精确的宇宙学关联函数并与共形微扰理论比较。在欧几里得形式下，先计算重整化的球面配分函数以及热算子和类后代算子的精确两点函数，再解析延拓到洛伦兹dS₂。分析了自旋和无序算子的两点函数，得出对其晚期标度维数的非微扰约束。两种情况都将精确结果与共形微扰理论比较，表明晚期发散的长期项破坏微扰级数。德西特伊辛模型明确展示了非微扰宇宙学可观测量中晚期微扰病态如何被重整化，为德西特空间中的量子场论动力学提供了一个最小可解的实验室。
英文摘要
We study the two-dimensional Ising model deformed by the relevant thermal operator and placed on de Sitter (dS) spacetime. Despite being strongly interacting in its original formulation, the theory is exactly solvable on account of fermionisation. We compute exact cosmological correlators and compare them with conformal perturbation theory. In the Euclidean formulation of the model, we first compute the renormalised sphere partition function and the exact two-point functions of the thermal operator and descendant-like operators. We analytically continue the two-point functions to Lorentzian dS$_2$. Their late-time behaviour is governed by de Sitter representation theory and includes oscillations associated with principal-series scaling dimensions. We then analyse two-point functions of the spin and disorder operators, which are non-local in the fermionic variables, and derive non-perturbative constraints on their late-time scaling dimensions. In both cases, we compare the exact answers to conformal perturbation theory (CPT) and we show that divergent secular terms generically spoil the perturbative series at late times. The de Sitter Ising model shows explicitly how late-time perturbative pathologies are resummed in non-perturbative cosmological observables and provides a minimal solvable laboratory for quantum field theory dynamics in de Sitter space.
Comments27 pages + appendix, 5 figures
