标题： 热场论中的角分形 显示英文标题

标题： Angular fractals in thermal QFT

摘要： 我们证明了热力学有效场论控制了$d$维QFT的配分函数的长距离展开，并且插入了任何有限阶的空间对称性。 因此，球面上的热力学配分函数作为角扭曲的函数表现出类似分形的结构，类似于模形式在实轴附近的特性。 作为一个示例应用，我们发现对于CFTs，在高温下偶自旋减奇自旋算符的有效自由能比通常的自由能小一个$1/2^d$因子。 在某些有理角度附近，配分函数从热力学EFT中的“Kaluza-Klein涡旋缺陷”中获得次级贡献，我们对此进行了分类。 我们通过自由理论和全息理论中的例子说明了我们的结果，并讨论了来自世界线瞬子的非微扰修正。 显示英文摘要

摘要： We show that thermal effective field theory controls the long-distance expansion of the partition function of a $d$-dimensional QFT, with an insertion of any finite-order spatial isometry. Consequently, the thermal partition function on a sphere displays a fractal-like structure as a function of angular twist, reminiscent of the behavior of a modular form near the real line. As an example application, we find that for CFTs, the effective free energy of even-spin minus odd-spin operators at high temperature is smaller than the usual free energy by a factor of $1/2^d$. Near certain rational angles, the partition function receives subleading contributions from "Kaluza-Klein vortex defects" in the thermal EFT, which we classify. We illustrate our results with examples in free and holographic theories, and also discuss nonperturbative corrections from worldline instantons.