Pseudoduality in Sigma Models

TL;DR

This paper explores pseudoduality in two-dimensional conformal sigma models, revealing that dual models have opposite 1-loop beta functions and establishing a natural pseudoduality transformation between solutions on different Lie groups, preserving stress-energy tensors.

Contribution

It introduces a new pseudoduality transformation between sigma models on different Lie groups, including non-isomorphic pairs, and shows its implications for conserved currents and renormalization group behavior.

Findings

Dual sigma models have opposite 1-loop beta functions.

A natural pseudoduality transformation exists for compact Lie groups of the same dimension.

The transformation preserves the stress-energy tensor and enables new conserved currents.

Abstract

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 B_n and C_n 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 G-tilde.