We revisit classical "on shell" duality, i.e., pseudoduality, in two-dimensional conformally invariant classical sigma models and find some new interesting results. We show that any two sigma models that are "on shell" duals have opposite 1-loop renormalization group beta functions because of the integrability conditions for the pseudoduality transformation. A new result states for any two compact Lie groups of the same dimension there is a natural pseudoduality transformation that maps classical solutions of the WZW model on the first group into solutions of the WZW model on the second group. This transformation preserves the stress-energy tensor. The two groups can be non-isomorphic such as Bl and Cl in the Cartan notation. This transformation can be used for a new construction of non-local conserved currents. The new non-local currents on G depend on the choice of dual group G̃.
ASJC Scopus subject areas
- Nuclear and High Energy Physics