Celestial CFT from CHY Formalism: Center Charge and Finite Size Effect

Scattering amplitudes in gauge theories can be calculated either by bulk theories in 4d Minkowski space-time($Mink_4$), or perceived as the correlation functions in celestial CFT(CCFT) living in the celestial sphere at null infinity, where an infinite-dimensional asymptotic symmetry, BMS group, resides. Another well developed method is the CHY formalism, which formulates the scattering amplitude in terms of the correlation functions on a 2d world sheet, on which an ambitwistor string theory is defined. The relationship between CHY theory and CCFT is encoded in scattering equations, which are algebraic equations lacking of analytical solutions in general. So we start from the CHY formalism, take the collinear limit, then find a nice operator formalism for the CCFT. In particular, the center charge $c$ is calculated to be 36 for the CCFT related to the 4d Yang-Mills theory. It then follows that the 4d cosmological constant naturally arises as the finite size effect in 2d CCFT, which is calculated by the method of the $T\bar{T}$ perturbed CCFT.