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arXiv · 2105.03530

Thermal one-point functions and single-valued polylogarithms

Anastasios C. Petkou
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Abstract

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 U(1) 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 parametrize 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 U(1) 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.

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Anastasios C. Petkou. 2021-05-07. Thermal one-point functions and single-valued polylogarithms. https://doi.org/10.1016/j.physletb.2021.136467

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