Exact Duality Symmetries in CFT and String Theory

TL;DR

This work demonstrates that exact duality symmetries in string theory and CFT extend beyond simple semiclassical settings, by embedding dualities as Weyl transformations of affine current algebras in WZW models and propagating them through compact cosets to give robust $O(d,d)$ structures. It shows that, for compact cases, dualities act as affine Weyl group symmetries with full $W_G\times W_G$ invariance on the spectrum and partition function, and that axial-vector dualities in abelian cosets are exact, enabling generation of new conformal backgrounds via $O(d,d,\mathbb{R})$ (and discrete $O(d,d,\mathbb{Z})$) actions. The paper also connects current-current marginal perturbations to $O(2d,2d)$ transformations, illustrating how such deformations can be organized within the duality framework. In non-compact cosets, evidence from minisuperspace and simple models suggests that affine-Weyl-like dualities may persist, though issues of positivity and spacetime interpretation remain subtler; overall, the work unifies duality concepts across compact and non-compact backgrounds and clarifies how they constrain the structure of consistent string backgrounds and perturbations.

Abstract

There is substancial overlap with hepth-9211081. More results are presented for duality in the non-compact case. It is argued that duality persists as a symmetry also in that case.