A new Wilson line-based classical action for gluodynamics

Abstract

We develop a new classical action that in addition to \mathrm{MHV}MHV vertices contains also \mathrm{N^kMHV}NkMHV vertices, where 1\leq k \leq n-41≤k≤n−4 with nn the number of external legs. The lowest order vertex is the four-point MHV vertex – there is no three point vertex and thus the amplitude calculation involves fewer vertices than in the CSW method. The action is obtained by a canonical transformation of the Yang-Mills action in the light-cone gauge, where the field transformations are based on Wilson line functionals.

Wilson lines and boundary operators of BCFW shifts

“…Later, following the idea of Britto-Cachazo-Feng-Witten (BCFW) recursion relation [11,12], the recursive structure of off-shell amplitudes is interpreted as a BCFW-like recursion relation by performing a complex shift of the Wilson line slope instead of the original momentum shift [13]. Furthermore, the Maximal-Helicity-Violating (MHV) vertices or MHV Lagrangian [14][15][16] in Cachazo-Svrcek-Witten (CSW) method [17] are shown to be connected to the straight infinite Wilson line on complex plane [18][19][20][21], in which the Wilson line appears as the field transformation between Yang-Mills theory and MHV Lagrangian. Besides, Wilson line operators also provide an useful bridge connecting the classical double copy and BCJ double copy by replacing color factor in Wilson line with kinematic factor [22].…”