发表机构
J. Stefan Institute; Faculty of Mathematics and Physics, University of Ljubljana（约兰·斯特凡研究所; 卢布尔雅那大学数学物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过模性与AGT对应，将全息热传播子推广至非零能量，利用SO(8)对称性、Molien级数和模异常方程逐阶确定低温展开系数，并与近边界展开方法结果一致。
AI 中文摘要
我们将arXiv:2509.02226中基于模性的全息热传播子方法推广到物理相关的非零能量ω情形。通过AGT对应，该问题被映射为具有N_f=4个超多重态的N=2 SU(2)规范理论。开启ω激活了所有四个超多重态质量，因此完整的SO(8)味对称性约束低温展开，而非ω=0时保持未破缺的子群。结果，展开的构建块不再仅是Eisenstein级数，还包括Jacobi theta函数。我们利用这一事实，结合所得不变环的Molien级数和模异常方程，逐阶确定低温展开系数，在每一阶仅匹配Zamolodchikov q递推中的有限项。我们获得了传播子的低温展开，并与完全不同的方法——体波动方程的近边界展开——的结果一致。
英文摘要
We extend the modularity-based approach of arXiv:2509.02226 for the holographic thermal propagator to the physically relevant case of nonzero energy $ω$. Via the AGT correspondence, the problem is mapped to $\mathcal{N}=2$ $SU(2)$ gauge theory with $N_f=4$ hypermultiplets. Turning on $ω$ activates all four hypermultiplet masses, so that the full $SO(8)$ flavor symmetry constrains the low-temperature expansion, rather than the subgroup left unbroken at $ω=0$. As a result, the building blocks of the expansion are no longer just Eisenstein series but also Jacobi theta functions. We use this fact, together with the Molien series of the resulting invariant ring and the modular anomaly equation, to fix the low-temperature expansion coefficients order by order, matching only a finite number of terms in the Zamolodchikov's $q$-recursion at each order. We obtain the low-temperature expansion of the propagator and find agreement with the result of a completely different method, the near-boundary expansion of the bulk wave equation.
Comments23 pages
