  We construct a moduli space of stable maps with fields associated to a triple
$(X,E,s)$ of a projective variety (or a DM stack with projective moduli space)
a vector bundle and a section. We show the class coincides up to a sign with
the virtual fundamental class on the moduli space of stable maps to
$Z=Z(s)\subset X$. We show that this gives a generalization of the Quantum
Lefschetz hyperplane principle. This generalizes similar comparison results of
Chang--Li, Kim--Oh and Chang--Li and presents a different approach from
Chen--Janda--Webb.
