The deformed Donaldson-Thomas (dDT) connection is a Hermitian connection of a Hermitian line bundle over a -manifold satisfying certain nonlinear PDEs. This is considered to be the mirror of a calibrated (associative) submanifold via mirror symmetry. As the name indicates, the dDT connection can also be considered as an analogue of the Donaldson-Thomas connection (-instanton).

In this talk, after reviewing these backgrounds, I will show that dDT connections indeed have properties similar to associative submanifolds and -instantons. I would also like to present some related problems. This is joint work with Hikaru Yamamoto.