Penrose limits of Lie Branes and a Nappi-Witten braneworld

Departing from the observation that the Penrose limit of AdS₃ × S³ is a group contraction in the sense of Inönü and Wigner, we explore the relation between the symmetric D-branes of AdS ₃ × S³ 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 AdS₂ × S² D3-brane in AdS₃ × 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.