$d>2$中的操作员热处理：惠更斯或复苏
Operator thermalisation in $d>2$: Huygens or resurgence
摘要：
即使在自由场论中，大多数复合算符的关联函数在非零温度下也随时间呈指数衰减。这种见解最近被编入OTH（操作员热化假说）。我们重新考虑一个早期的例子，大$N$自由场受到单态约束。本研究在尺寸$d>2$激励技术修改的原始OTH，以允许广义自由字段。此外，惠更斯原理，有效的波动方程，只有在偶数维，导致不同的热化。当惠更斯原理适用时，它直接起作用，但如果不适用，热化作用就更加难以捉摸。相反，在奇数维，我们发现一个链接到复苏理论，注意到指数松弛类似于非微扰修正的渐近微扰展开。在没有应用复苏技术的力量的情况下，我们仍然在奇数维中找到了对热化的支持，尽管这些论点是不完整的。
英文摘要：
Correlation functions of most composite operators decay exponentially with time at non-zero temperature, even in free field theories. This insight was recently codified in an OTH (operator thermalisation hypothesis). We reconsider an early example, with large $N$ free fields subjected to a singlet constraint. This study in dimensions $d>2$ motivates technical modifications of the original OTH to allow for generalised free fields. Furthermore, Huygens' principle, valid for wave equations only in even dimensions, leads to differences in thermalisation. It works straightforwardly when Huygens' principle applies, but thermalisation is more elusive if it does not apply. Instead, in odd dimensions we find a link to resurgence theory by noting that exponential relaxation is analogous to non-perturbative corrections to an asymptotic perturbation expansion. Without applying the power of resurgence technology we still find support for thermalisation in odd dimensions, although these arguments are incomplete.
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