  We study the moduli space of torsion-free G2-structures on a fixed compact
manifold, and define its associated universal intermediate Jacobian J. We
define the Yukawa coupling and relate it to a natural pseudo-Kahler structure
on J. We consider natural Chern-Simons type functionals, whose critical points
give associative and coassociative cycles (calibrated submanifolds coupled with
Yang-Mills connections), and also deformed Donaldson-Thomas connections. We
show that the moduli spaces of these structures can be isotropically immersed
in J by means of G2-analogues of Abel-Jacobi maps.
