  In this paper, we solve the problem of giving a gauge-theoretic description
of the natural Dirac structure on a Lie Group which plays a prominent role in
the theory of D- branes for the Wess-Zumino-Witten model as well as the theory
of quasi-Hamiltonian spaces. We describe the structure as an
infinite-dimensional reduction of the space of connections over the circle. Our
insight is that the formal Poisson structure on the space of connections is not
an actual Poisson structure, but is itself a Dirac structure, due to the fact
that it is defined by an unbounded operator. We also develop general tools for
reducing Courant algebroids and morphisms between them, allowing us to give a
precise correspondence between Hamiltonian loop group spaces and quasi-
Hamiltonian spaces.
