We study the moduli space M of torsion-free G2-structures on a fixed compact manifold M7,
and define its associated universal intermediate Jacobian J . We define the Yukawa coupling and
relate it to a natural pseudo-K¨ahler 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.