Thermal CFTs in momentum space

Andrea Manenti
SPRINGER, 2020
Article

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(phi) + l + 2n. By analytically continuing to Lorentzian signature we show that the spectral density at high spatial momenta has support on the spectrum condition |omega| > |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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Andrea Manenti
SPRINGER, 2020
Article

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https://infoscience.epfl.ch/record/275641?ln=fr

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Joachim Krieger, Shuang Miao

We exhibit non-equivariant perturbations of the blowup solutions constructed in [18] for energy critical wave maps into

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We define form factors and scattering amplitudes in Conformal Field Theory as the coefficient of the singularity of the Fourier transform of time-ordered correlation functions, as p(2) -> 0. In particular, we study a form factor F(s, t, u) obtained from a four-point function of identical scalar primary operators. We show that F is crossing symmetric, analytic and it has a partial wave expansion. We illustrate our findings in the 3d Ising model, perturbative fixed points and holographic CFTs.

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