Mukai duality on adiabatic coassociative fibrations

This paper studies the formal adiabatic limit of coassociative K3 fibred torsion free $G_2$ manifolds fibred over a contractible base, shows how to put this structure on a different fibration obtained by fibrewise performing Mukai duality of K3 surfaces, and furthermore relates the gauge theories on both fibrations by a Nahm transform. This gives a mathematical interpretation to the physical speculations of Gukov, Yau and Zaslow.