Supersymmetric Godel Universes in String Theory

TL;DR

This paper systematically constructs and analyzes supersymmetric Gödel Universes within string and M-theory. It demonstrates that not only T-duality but also type IIA/M-theory S-duality can map pp-waves to Gödel backgrounds, and it identifies a novel 18-supersymmetry M-theory Gödel background not evidently dual to a pp-wave. By exploring $G_{2n+1}$ backgrounds for $n=1$ to $5$, the authors reveal intricate duality webs, interpolating solutions between Gödel universes and pp-waves, and they provide explicit string spectra for two type IIA Gödel Universes as well as D-brane configurations and their supergravity realizations. The work advances our understanding of highly supersymmetric, closed-time-like-curve spacetimes in string theory and sets the stage for potential holographic interpretations, while also raising questions about the full consistency and physical meaning of strings on Gödel backgrounds.

Abstract

Supersymmetric backgrounds in string and M-theory of the Godel Universe type are studied. We find several new Godel Universes that preserve up to 20 supersymmetries. In particular, we obtain an interesting Godel Universe in M-theory with 18 supersymmetries which does not seem to be dual to a pp-wave. We show that not only T-duality but also the type-IIA/M-theory S-duality can give supersymmetric Godel Universes from pp-waves. We find solutions that can interpolate between Godel Universes and pp-waves. We also compute the string spectrum on two type IIA Godel Universes. Furthermore, we obtain the spectrum of D-branes on a Godel Universe and find the supergravity solution for a D4-brane on a Godel Universe.

Figures (1)

• Figure 1: Diagram that shows connection between T and S-duality transformations relating Gödel Universes and pp-waves.