Abstract
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.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
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