Physics Letters B ( IF 4.4 ) Pub Date : 2021-06-23 , DOI: 10.1016/j.physletb.2021.136467 Anastasios C. Petkou
I point out that the thermal one-point functions of a pair of relevant operators in massive free QFTs, in odd dimensions and in the presence of an imaginary chemical potential for a global charge, are given by certain classes of single-valued polylogarithms. This result is verified by a direct calculation using the thermal OPE. The complex argument of the polylogarithms parametrizes a two-dimensional subspace of relevant deformations of generalised free CFTs, while the rank of the polylogarithms is related to the dimension d. This may be compared with the well-known representation of single-valued polylogarithms as multiloop Feynman amplitudes. As an example, the thermal one-point function of the charge in d-dimensions generalises the thermal average of the twist operator in a pair of harmonic oscillators and is given by the well-known conformal ladder graphs in four dimensions.
中文翻译:
热单点函数和单值多对数
我指出,在大量自由 QFT 中,在奇维数和存在假想化学势的情况下,一对相关算子的热单点函数 全局电荷由某些类别的单值多对数给出。该结果通过使用热 OPE 的直接计算得到验证。多对数的复数参数参数化了广义自由 CFT 的相关变形的二维子空间,而多对数的等级与维度d 相关。这可以与众所周知的将单值多对数表示为多环费曼振幅进行比较。例如,热单点函数d维中的电荷概括了一对谐振子中扭曲算子的热平均值,并由众所周知的四维共形梯形图给出。