Penrose limits of Lie Branes and a Nappi--Witten braneworld

TL;DR

This paper investigates how symmetric D-branes in AdS_3 x S^3 relate to those in its Penrose limit, a plane wave background, revealing new brane configurations and criteria for plane wave isometries to Lorentzian Lie groups.

Contribution

It characterizes symmetric D-branes in the Penrose limit of AdS_3 x S^3 and establishes a criterion for plane wave isometries to Lorentzian Lie groups, including new brane solutions.

Findings

Existence of a space-filling D5-brane in the plane wave background.

Identification of a foliation by D3-branes with Nappi--Witten geometry.

Maximally supersymmetric IIB plane wave is isometric to a Lorentzian Lie group.

Abstract

Departing from the observation that the Penrose limit of AdS_3 x S^3 is a group contraction in the sense of Inonu and Wigner, we explore the relation between the symmetric D-branes of AdS_3 x S^3 and those of its Penrose limit, a six-dimensional symmetric plane wave analogous to the four-dimensional Nappi--Witten spacetime. Both backgrounds are Lie groups admitting bi-invariant lorentzian metrics and symmetric D-branes wrap their (twisted) conjugacy classes. We determine the (twisted and untwisted) symmetric D-branes in the plane wave background and we prove the existence of a space-filling D5-brane and, separately, of a foliation by D3-branes with the geometry of the Nappi--Witten spacetime which can be understood as the Penrose limit of the AdS_2 x S^2 D3-brane in AdS_3 x S^3. Parenthetically we also derive a simple criterion for a symmetric plane wave to be isometric to a lorentzian Lie group. In particular we observe that the maximally supersymmetric plane wave in IIB string theory is isometric to a lorentzian Lie group, whereas the one in M-theory is not.