Plane Wave Limits and T-Duality

TL;DR

The paper extends the Penrose limit to all solutions in string theories, showing they can be approximated by plane waves that preserve some supersymmetry and are compatible with T-duality, providing a unified approach to analyzing string backgrounds.

Contribution

It introduces a generalized Penrose limit applicable to all low-energy solutions in string theories that preserves T-duality and supersymmetry, unifying various limiting procedures.

Findings

Any low-energy string solution has a plane wave limit.

The limit commutes with T-duality, preserving duality relations.

Plane wave limits always preserve some supersymmetry.

Abstract

The Penrose limit is generalized to show that, any leading order solution of the low-energy field equations in any one of the five string theories has a plane wave solution as a limit. This limiting procedure takes into account all the massless fields that may arise and commutes with the T-duality so that any dual solution has again a plane wave limit. The scaling rules used in the limit are unique and stem from the scaling property of the D=11 supergravity action. Although the leading order solutions need not be exact or supersymmetric, their plane wave limits always preserve some portion of the Poincare supersymmetry and solve the relevant field equations in all powers of the string tension parameter. Further properties of the limiting procedure are discussed.