A Canonical Approach to Duality Transformations

TL;DR

This paper presents a canonical framework for target-space duality in string theory, showing that Buscher's abelian duality rules follow from a canonical transformation generated by $F=rac{1}{2}\oint ( heta' ilde{\theta}-\theta \tilde{\theta}') dσ$. By working in adapted coordinates with a Killing vector, it derives the dual background via $\tilde{g}_{00}=1/g_{00}$, $\tilde{g}_{0i}=-b_{0i}/g_{00}$, $\tilde{g}_{ij}=...$, $\tilde{b}_{ij}=...$, and $\tilde{\Phi}=\Phi-\log g_{00}$, and it analyzes how currents transform, including locality properties in the chiral case. The approach extends to WZW models, where the duality group becomes $Aut(G)_L\times Aut(G)_R$, but non-abelian duality presents obstacles that resist a full Hamiltonian treatment. Overall, the work argues that abelian duality can be understood through a minimal Hamiltonian lens, while non-abelian duality remains a challenging issue beyond this framework.

Abstract

We show that Buscher's abelian duality transformation rules can be recovered in a very simple way by performing a canonical transformation first suggested by Giveon, Rabinovici and Veneziano. We explore the properties of this transformation, and also discuss some aspects of non-abelian duality.