Plane Waves: To infinity and beyond!

TL;DR

The paper develops a causal-boundary perspective on plane-wave spacetimes by applying the Geroch–Kronheimer–Penrose construction of ideal points (TIPs/TIFs) to BFHP and more general plane waves. It shows that the BFHP boundary matches BN's conformal boundary, consisting of a one-dimensional null line ${\cal I}$ plus $i^+$ and $i^-$, with TIPs and TIFs identified along ${\cal I}$. For homogeneous plane waves with constant $\mu^2_{ij}$ and at least one positive eigenvalue, the ideal boundary remains a single null line parametrised by $x^+$, while backgrounds with no positive eigenvalues are generally unphysical in string theory, though special conformally flat cases yield different boundary structures. The analysis extends to time-dependent plane waves arising from Penrose limits of D$p$-branes, showing a robust 1D boundary structure in many cases and offering a framework to explore holographic duals beyond the maximally supersymmetric setup.

Abstract

We describe the asymptotic boundary of the general homogeneous plane wave spacetime, using a construction of the `points at infinity' from the causal structure of the spacetime as introduced by Geroch, Kronheimer and Penrose. We show that this construction agrees with the conformal boundary obtained by Berenstein and Nastase for the maximally supersymmetric ten-dimensional plane wave. We see in detail how the possibility to go beyond (or around) infinity arises from the structure of light cones. We also discuss the extension of the construction to time-dependent plane wave solutions, focusing on the examples obtained from the Penrose limit of Dp-branes.