Abstract
We study some aspects of conformal field theories at finite temperature in momentum space. We provide a formula for the Fourier transform of a thermal conformal block and study its analytic properties. In particular we show that the Fourier transform vanishes when the conformal dimension and spin are those of a “double twist” operator ∆ = 2∆ϕ + ℓ + 2n. By analytically continuing to Lorentzian signature we show that the spectral density at high spatial momenta has support on the spectrum condition |ω| > |k|. This leads to a series of sum rules. Finally, we explicitly match the thermal block expansion with the momentum space Green’s function at finite temperature in several examples.
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Manenti, A. Thermal CFTs in momentum space. J. High Energ. Phys. 2020, 9 (2020). https://doi.org/10.1007/JHEP01(2020)009
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DOI: https://doi.org/10.1007/JHEP01(2020)009