The Inner Branes

WZW models are abstract conformal field theories with an infinite dimensional symmetry which accounts for their integrability, and at the same time have a sigma model description of closed string propagation on Lie group manifolds which endows the models with an intuitive geometric meaning. We exploit this dual algebraic and geometric property of WZW models to provide an explicit example of new type of field-dependent reflection matrix for open-strings in Nappi-Witten model–a ppwave background supported by a null NS three-form flux. This reflection matrix, corresponding to a space-filling D-brane, arises from using an inner automorphism to glue the left-moving with the right-moving chiral currents at the boundary. Different choices of the inner automorphisms correspond to different background gauge field configurations. The reflection matrix is such that half of the infinite dimensional affine Kac-Moody symmetry present in the closed-string theory is preserved by a unique combination of the left and the right chiral currents.