A Note on D–brane — Anti–D–brane Interactions in Plane Wave Backgrounds

We study aspects of the interaction between a D–brane and an anti-D–brane in the maximally supersymmetric plane wave background of type IIB superstring theory, which is equipped with a mass parameter μ. An early such study in flat spacetime (μ = 0) served to sharpen intuition about D–brane interactions, showing in particular the key role of the “stringy halo” that surrounds a D–brane. The halo marks the edge of the region within which tachyon condensation occurs, opening a gateway to new non–trivial vacua of the theory. It seems pertinent to study the fate of the halo for non–zero μ. We focus on the simplest cases of a Lorentzian brane with p = 1 and an Euclidean brane with p = −1, the D–instanton. For the Lorentzian brane, we observe that the halo is unaffected by the presence of non–zero μ. This most likely extends to other (Lorentzian) p. For the Euclidean brane, we find that the halo is affected by non–zero μ. As this is related to subtleties in defining the exchange amplitude between Euclidean branes in the open string sector, we expect this to extend to all Euclidean branes in this background.