Weighted Laplacians, cocycles and recursion relations

Understand

Hodge's formula represents the gravitational MHV amplitude as the determinant of a minor of a certain matrix.

• When expanded, this determinant becomes a sum over weighted trees, which is the form of the MHV formula first obtained by Bern, Dixon, Perelstein, Rozowsky and rediscovered by Nguyen, Spradlin, Volovich and Wen.
• The gravity MHV amplitude satisfies the Britto, Cachazo, Feng and Witten recursion relation.
• The main building block of the MHV amplitude, the so-called half-soft function, satisfies a different, Berends-Giele-type recursion relation.