Supersymmetries and Hopf-duality in the Penrose Limit of AdS_3 times S^3 times T^4

TL;DR

This paper explores how Hopf-duality affects supersymmetry preservation in the Penrose limit of $AdS_3\times S^3\times T^4$ geometries, revealing variations in supersymmetry counts depending on the duality and geodesic directions.

Contribution

It provides a detailed analysis of supersymmetry preservation under Hopf-duality and different Penrose limits in D1/D5-brane systems, including the impact of tilted geodesics.

Findings

Penrose limit makes the internal torus size comparable to other directions.

Supersymmetries are preserved when the limit is along the torus direction.

Hopf-dualized geometry preserves only 4 supersymmetries.

Abstract

We investigate various aspects of the plane wave geometries obtained from D1/D5-brane system. We study the effect of Hopf-duality on the supersymmetries preserved by the Penrose limit of $AdS_3\times S^3\times T^4$ geometry. In type-IIB case, we first show that the Penrose limit makes the size of the `would-be' internal torus comparable to that of the other directions. Based on this observation, we consider, in taking the Penrose limit, the generalization of the null geodesic to incorporate the tilted direction between the equator of $S^3$ and one of the torus directions. For generic values of the tilting angle, supersymmetries are not preserved. When the limit is taken along the torus direction, 16 supersymmetries are preserved. For the ordinary Penrose limit, 16 generic and 8 `supernumerary' supersymmetries are observed. In the Penrose limit of Hopf-dualized type-IIA geometry, only 4 supersymmetries are preserved. We classify all the Killing spinors according to their periodic properties along some relevant coordinates.