Penrose Limits, the Colliding Plane Wave Problem and the Classical String Backgrounds

TL;DR

This paper explores Penrose limits in classical string backgrounds, relating colliding wave problems to string theory, and constructs solvable backgrounds with implications for quantum vacua in time-dependent settings.

Contribution

It introduces a novel approach using Szekeres form for Penrose limits, constructs new solvable backgrounds, and discusses quantum vacuum issues in time-dependent string backgrounds.

Findings

Penrose limits can uniquely determine target space under symmetry.

Constructed solvable backgrounds with exact string solutions.

Identified issues with singularities and quantum vacua in these backgrounds.

Abstract

We show how the Szekeres form of the line element is naturally adapted to study Penrose limits in classical string backgrounds. Relating the "old" colliding wave problem to the Penrose limiting procedure as employed in string theory we discuss how two orthogonal Penrose limits uniquely determine the underlying target space when certain symmetry is imposed. We construct a conformally deformed background with two distinct, yet exactly solvable in terms of the string theory on R-R backgrounds, Penrose limits. Exploiting further the similarities between the two problems we find that the Penrose limit of the gauged WZW Nappi-Witten universe is itself a gauged WZW plane wave solution of Sfetsos and Tseytlin. Finally, we discuss some issues related to singularity, show the existence of a large class of non-Hausdorff solutions with Killing Cauchy Horizons and indicate a possible resolution of the problem of the definition of quantum vacuum in string theory on these time-dependent backgrounds.