  Donaldson-Thomas theory on a Calabi-Yau can be described in terms of a
certain six-dimensional cohomological gauge theory. We introduce a certain
class of defects in this gauge theory which generalize surface defects in four
dimensions. These defects are associated with divisors and are defined by
prescribing certain boundary conditions for the gauge fields. We discuss
generalized instanton moduli spaces when the theory is defined with a defect
and propose a generalization of Donaldson-Thomas invariants. These invariants
arise by studying torsion free coherent sheaves on Calabi-Yau varieties with a
certain parabolic structure along a divisor, determined by the defect. We
discuss the case of the affine space as a concrete example. In this case the
moduli space of parabolic sheaves admits an alternative description in terms of
the representation theory of a certain quiver. The latter can be used to
compute the invariants explicitly via equivariant localization. We also briefly
discuss extensions of our work to other higher dimensional field theories.
