Exact Duality Symmetries in CFT and String Theory

TL;DR

This paper investigates the exact duality symmetries in conformal field theories and string theory, identifying affine Weyl transformations as the core symmetry, and discusses their implications for compact and non-compact models.

Contribution

It unifies the understanding of duality symmetries in WZW and coset models, showing they are exact symmetries in string theory for compact, unitary cases, and explores non-compact models.

Findings

Affine Weyl transformations underlie duality symmetries.

Dualities are exact symmetries in string theory to all orders for certain models.

Duality may not be a symmetry in non-compact models.

Abstract

The duality symmetries of WZW and coset models are discussed. The exact underlying symmetry responsible for semiclassical duality is identified with the symmetry under affine Weyl transformations. This identification unifies the treatement of duality symmetries and shows that in the compact and unitary case they are exact symmetries of string theory to all orders in $\alpha'$ and in the string coupling constant. Non-compact WZW models and cosets are also discussed. A toy model is analyzed suggesting that duality will not generically be a symmetry.