Penrose Limits of Non-standard Brane Intersections

TL;DR

This work analyzes Penrose limits of the non-standard brane intersection yielding $AdS_3\times S^3\times S^3\times S^1$, uncovering a one-parameter family of pp-waves from rotating the internal $S^1$ fibrations. It shows that 16 standard Killing spinors are always present, while 4 supernumerary Killing spinors arise only at $\alpha=\frac{\pi}{4}$, enabling a light-cone string action with linearly realized supersymmetry. The authors further relate the pp-waves to $S^1$-wrapped D3-branes via T-duality and S-duality and extend the construction to various other non-standard intersections producing AdS$_3$ or AdS$_2$ factors with multiple constant fluxes. The results provide exactly solvable string backgrounds in rich flux geometries and illustrate the role of internal rotations in modulating supersymmetry. These insights are connected through dualities to M-theory pp-waves and point to a broader landscape of tractable non-standard brane intersections.

Abstract

The non-standard intersection of two 5-branes and a string can give rise to AdS_3\times S^3\times S^3\times S^1. We consider the Penrose limit of this geometry and study the supersymmetry of the resulting pp-wave solution. There is a one-parameter family of Penrose limits associated with the orthogonal rotation of the two foliating circles within the two 3-spheres. Supernumerary Killing spinors arise only when the rotation angle is 45 degrees, for which case we obtain the corresponding light-cone string action that has linearly-realised supersymmetry. We also obtain Penrose limits of other non-standard intersections that give rise to the product of AdS_3 or AdS_2 and two spheres. The resulting pp-waves are supported by multiple constant field strengths.