(Twisted) Toroidal Compactification of pp-Waves

TL;DR

This paper explores various compactifications of maximally supersymmetric type IIB pp-waves on tori with twists, analyzing supersymmetry preservation and discussing dualities and related backgrounds.

Contribution

It systematically classifies supersymmetry-preserving compactifications of pp-waves on tori with twists and discusses their worldsheet theories and dual solutions.

Findings

Compactifications preserve 16 to 24 supercharges depending on the torus dimension and twist.

Explicit T-dual and decompactified solutions in type IIA and M-theory are provided.

Comments on AdS/CFT correspondence implications are included.

Abstract

The maximally supersymmetric type IIB pp-wave is compactified on spatial circles, with and without an auxiliary rotational twist. All spatial circles of constant radius are identified. Without the twist, an S$^1$ compactification can preserve 24, 20 or 16 supercharges. $T^2$ compactifications can preserve 20, 18 or 16 supercharges; $T^3$ compactifications can preserve 18 or 16 supercharges and higher compactifications preserve 16 supercharges. The worldsheet theory of this background is discussed. The T-dual and decompactified type IIA and M-theoretic solutions which preserve 24 supercharges are given. Some comments are made regarding the AdS parent and the CFT description.