D-branes in curved spacetime: Nappi-Witten background

TL;DR

This work bridges boundary-state and sigma-model viewpoints for D-branes in the Nappi–Witten NW curved background. By solving exact boundary conditions on the NW WZW model, the authors classify two families of boundary states, $R_I$ and $R_{II}$, and interpret them as D3/D1 and Euclidean D0 branes, with detailed geometric embeddings and induced metrics. They show how T-duality connects these branes via explicit $T_I$ and $T_{II}$ transformations and connect the boundary-state data to static Born–Infeld solutions. The relation to the sigma-model boundary conditions reveals a field-dependent boundary matrix $M$ that reduces to the boundary-state automorphisms in special cases, establishing a coherent picture that links worldsheet conformal structure with spacetime D-brane geometry in a curved, exactly solvable background. The analysis also discusses N=2 extensions and underscores the interplay between current-algebra, BI actions, and worldvolume embeddings in NW spacetime.

Abstract

We find exact D-brane configurations in the Nappi-Witten background using the boundary state approach and describe how they are related by T-duality transformations. We also show that the classical boundary conditions of the associated sigma model correspond to a field dependent automorphism relating the chiral currents and discuss the correspondence between the boundary state approach and the sigma model approach.

Figures (1)

• Figure 1: $x^0=\tau=0$ snapshots for $\varrho=1,2,5,10,20,50,100$.