Branes in AdS and pp-wave spacetimes
Kostas Skenderis, Marika Taylor
TL;DR
The paper develops a comprehensive framework for half-supersymmetric AdS embeddings in $AdS_5\times S^5$, corresponding to quarter-BPS D3-Dp intersections, and includes the notable Karch-Randall $AdS_4\times S^2$ case. It proves supersymmetry via explicit kappa-symmetry projections, explores holographic AdS/dCFT interpretations with defect RG flows, and analyzes the pp-wave limit to produce half-supersymmetric D-branes in the pp-wave background. A broad classification of D-brane embeddings in both AdS and pp-wave settings is presented, including rotating branes, giant gravitons, and instantonic configurations, along with a detailed map to defect-field theory operators in the BMN limit. These results illuminate the defect-sector holography and provide a dictionary between bulk D-brane configurations and boundary defect degrees of freedom, with potential applications to non-perturbative states and RG flows in the dual theories.
Abstract
We find half supersymmetric AdS-embeddings in AdS_5 x S^5 corresponding to all quarter BPS orthogonal intersections of D3-branes with Dp-branes. A particular case is the Karch-Randall embedding AdS_4 x S^2. We explicitly prove that these embeddings are supersymmetric by showing that the kappa symmetry projections are compatible with half of the target space Killing spinors and argue that all these cases lead to AdS/dCFT dualities involving a CFT with a defect. We also find an asymptotically AdS_4 x S^2 embedding that corresponds to a holographic RG-flow on the defect. We then consider the pp-wave limit of the supersymmetric AdS-embeddings and show how it leads to half supersymmetric D-brane embeddings in the pp-wave background. We systematically analyze D-brane embeddings in the pp-wave background along with their supersymmetry. We construct all supersymmetric D-branes wrapped along the light-cone using operators in the dual gauge theory: the open string states are constructed using defect fields. We also find supersymmetric D1 (monopoles) and D3 (giant gravitons) branes that wrap only one of the light-cone directions. These correspond to non-perturbative states in the dual gauge theory.