Quantization of heterotic strings in a Goedel/Anti de Sitter spacetime and chronology protection

TL;DR

This work constructs an exact Gödel-like deformation of $AdS_3$ within heterotic string theory as an asymmetric, marginal deformation of the $SL(2,\mathbb{R})_k$ CFT, demonstrating conformal invariance to all orders and enabling an exact string spectrum and genus-one partition function. It shows that long strings winding around the resulting closed timelike curves destabilize the background by acquiring tachyonic-like excitations, while short strings remain well-behaved near the core; the authors propose a stringy chronology-protection mechanism via the condensation of a ring of fundamental strings, described by a second marginal deformation that renders the problematic region singular but stabilizes the spectrum. The analysis includes a no-ghost theorem extended to the Gödel/AdS$_3$ background, a modular-invariant one-loop amplitude, and a physical picture of how a stringy endpoint could resolve causality violations, with potential holographic interpretations discussed. Overall, the paper provides a concrete, exact CFT framework to study chronology protection and tachyon-driven instabilities in Gödel-like spacetimes within string theory.

Abstract

We show that a Goedel-like deformation of AdS3 in heterotic string theory can be realized as an exact string background. Indeed this class of solutions is obtained as an exactly marginal deformation of the conformal field theory describing the NS5/F1 heterotic background. It can also be embedded in type II superstrings as a Kaluza-Klein reduction. We compute the spectrum of this model as well as the genus one modular invariant partition function. We discuss the issue of closed timelike curves and the propagation of long strings. They destabilize completely the background, although we construct another exact string background that may describe the result of the condensation of these long strings. Closed timelike curves are avoided in that case.