  WZW models are abstract conformal field theories with an infinite dimensional
symmetry which accounts for their integrability, and at the same time they have
a sigma model description of closed string propagation on group manifolds
which, in turn, endows the models with an intuitive geometric meaning. We
exploit this dual algebraic and geometric property of WZW models to construct
an explicit example of a field-dependent reflection matrix for open-strings in
Nappi-Witten model. Demanding the momentum outflow at the boundary to be zero
determines a certain combination of the left and right chiral currents at the
boundary. This same reflection matrix is obtained algebraically from an inner
automorphism, giving rise to a space-filling D-brane. Half of the infinite
dimensional affine Kac-Moody symmetry present in the closed-string theory is
preserved by this unique combination of the left and the right chiral currents.
The OPEs of these boundary currents are computed explicitly and they are showed
to obey the same current algebra as those of the closed-string chiral currents.
Different choices of the inner automorphisms correspond to different background
gauge field configurations. Only those B-field configurations, and the
corresponding D-branes, that preserve the diagonal part of the infinite
dimensional chiral algebras are allowed. In this way the existence of the
D-branes in curved spaces is further constrained by the underlying symmetry of
the ambient spacetime.
