Kaigorodov spaces and their Penrose limits

TL;DR

This paper studies Kaigorodov spaces as near horizon limits of branes, derives their Penrose limits, analyzes symmetries, and explores solvable string backgrounds, revealing how perturbations behave under these limits.

Contribution

It provides the first detailed analysis of Penrose limits of Kaigorodov spaces and their symmetry properties, including the occurrence of Inonu-Wigner contractions and symmetry enhancements.

Findings

Penrose limits of Kaigorodov spaces lead to solvable string backgrounds.

Symmetry analysis reveals Inonu-Wigner contractions and unexpected enhancements.

Perturbations on branes persist in limits but tend to decouple, resulting in homogeneous plane-wave backgrounds.

Abstract

Kaigorodov spaces arise, after spherical compactification, as near horizon limits of M2, M5, and D3-branes with a particular pp-wave propagating in a world volume direction. We show that the uncompactified near horizon configurations K\times S are solutions of D=11 or D=10 IIB supergravity which correspond to perturbed versions of their AdS \times S analogues. We derive the Penrose-Gueven limits of the Kaigorodov space and the total spaces and analyse their symmetries. An Inonu-Wigner contraction of the Lie algebra is shown to occur, although there is a symmetry enhancement. We compare the results to the maximally supersymmetric CW spaces found as limits of AdS\times S spacetimes: the initial gravitational perturbation on the brane and its near horizon geometry remains after taking non-trivial Penrose limits, but seems to decouple. One particuliar limit yields a time-dependent homogeneous plane-wave background whose string theory is solvable, while in the other cases we find inhomogeneous backgrounds.