Clebsch (string) decomposition in d=3 field theory

Abstract

We study the applicability of the intrinsically nonlinear Clebsch vector field decomposition into three scalars in the description of d=3 field theories. In particular, we note and account for the incompleteness of this parameterization when attempting to use it in variational principles involving Maxwell and Chern–Simons actions. Similarities with string decomposition of metrics and their actions are also pointed out.

Additional details