N=4 Supersymmetric Yang-Mills theory in soft-collinear effective theory

We formulate N=4 supersymmetric Yang-Mills theory in terms of soft-collinear effective theory. The effective Lagrangian in soft-collinear effective theory is developed according to the power counting by a small parameter \eta \sim p_{\perp}/Q. All the particles in this theory are in the adjoint representation of the SU(N) gauge group, and we derive the collinear gauge-invariant Lagrangian in the adjoint and fundamental representations respectively. We consider collinear and ultrasoft Wilson lines in this theory, and show the ultrasoft factorization of the collinear Lagrangian by redefining the collinear fields with the use of the ultrasoft Wilson lines. The vertex correction for a vector fermion current at one loop is explicitly presented as an example to illustrate how the computation is performed in the effective theory.