Diagonal D-branes in product spaces and their Penrose limits

TL;DR

This paper investigates diagonal D-branes in complex AdS and sphere backgrounds, analyzing their embeddings, flux configurations, and Penrose limits, revealing new brane types and behaviors in pp-wave geometries.

Contribution

It introduces new classes of diagonal D-branes with mixed embeddings and fluxes, and explores their Penrose limits, including nontrivial relativistic pulses and oblique embeddings.

Findings

Diagonal branes wrap calibrated and non-supersymmetric cycles.

Mixed flux stabilizes certain non-supersymmetric branes.

Penrose limits produce branes with relativistic pulses and oblique embeddings.

Abstract

We study classes of D-branes embedded in various AdS^m x S^n x S^p x T^q backgrounds, which nontrivially mix the target-space submanifolds. Mixing is achieved either via diagonal geometric embedding or through a mixed worldvolume flux which has one index in the sphere and one index in the AdS part. Branes of the former type wrap calibrated cycles in the target space, while those of the latter type wrap non-supersymmetric target space cycles which are stabilised only after the mixed worldvolume flux is turned on. In the second part of the paper we study two qualitatively different Penrose limits of these diagonal branes. In the first case we look at geodesics which do not belong to the worldvolume of brane. In order to get a nontrivial result, one needs to bring the brane closer and closer to the geodesic while taking the limit. The result is a D-brane with a worldvolume relativistic pulse. In the second case the Penrose geodesic belongs to the worldvolume and the resulting brane is of the ``oblique'' type: it is diagonally embedded between different SO groups of the target space pp-wave.