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The Hellings and Downs correlation curve describes the correlation of thetiming residuals from pairs of pulsars as a function of their angularseparation on the sky and is a smoking-gun signature for the detection of anisotropic stochastic background of gravitational waves. We show that it can beeasily obtained from realizing that Lorentz transformations are conformaltransformations on the celestial sphere and from the conformal properties ofthe two-point correlation of the timing residuals. This result allows severalgeneralizations, e.g. the calculation of the three-point correlator of the timeresiduals and the inclusion of additional polarization modes (vector and/orscalar) arising in alternative theories of gravity.

The PTA Hellings and Downs Correlation Unmasked by Symmetries