  In this note, we investigate relations between tree-level off-shell currents
in nonlinear sigma model. Under Cayley parametrization, all odd-point currents
vanish. We propose and prove a generalized $U(1)$ identity for even-point
currents. The off-shell $U(1)$ identity given in [1] is a special case of the
generalized identity studied in this note. The on-shell limit of this identity
is equivalent with the on-shell KK relation. Thus this relation provides the
full off-shell correspondence of tree-level KK relation in nonlinear sigma
model.

High Energy Physics - Theory