Inner brane: A D3-brane in Nappi-Witten space from an inner automorphism

Abstract

Wess-Zumino-Witten (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 the 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 operator-product expansions of these boundary currents are computed explicitly and they are shown 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.