MHV Gluon Scattering Amplitudes from Celestial Current Algebras

Understand

We show that the Mellin transform of an $n$-point tree level MHV gluon scattering amplitude, also known as the celestial amplitude in pure Yang-Mills theory, satisfies a system of $(n-2)$ linear first order partial differential equations corresponding to $(n-2)$ positive helicity gluons.

• Although these equations closely resemble Knizhnik-Zamolodchikov equations for $SU(N)$ current algebra there is also an additional "correction" term coming from the subleading soft gluon current algebra.
• These equations can be used to compute the leading term in the gluon-gluon OPE on the celestial sphere.
• Similar equations can also be written down for the momentum space tree level MHV scattering amplitudes.