  We consider finite deformations of the Hull--Strominger system. Starting from
the heterotic superpotential, we identify complex coordinates on the off-shell
parameter space. Expanding the superpotential around a supersymmetric vacuum
leads to a third-order Maurer--Cartan equation that controls the moduli. The
resulting complex effective action generalises that of both Kodaira--Spencer
and holomorphic Chern--Simons theory. The supersymmetric locus of this action
is described by an $L_3$ algebra.
