  We generalize the CHY formalism to one-loop level, based on the framework of
the null string theory. The null string, a tensionless string theory, produces
the same results as the ones from the chiral ambitwistor string theory, with
the latter believed to give a string interpretation of the CHY formalism. A key
feature of our formalism is the interpretation of the modular parameters. We
find that the $S$ modular transformation invariance of the ordinary string
theory does not survive in the case of the null string theory. Treating the
integration over the modular parameters this way enable us to derive the n-gons
scattering amplitude in field theory, thus proving the n-gons conjecture.
