Pseudoduality in Sigma Models

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.

28 pages, LaTeX file

References in corpus (5)

• Local conserved charges in principal chiral models
• Conserved charges and supersymmetry in principal chiral and WZW models
• Target Space Duality I: General Theory
• Target Space Duality II: Applications
• Target Space Pseudoduality Between Dual Symmetric Spaces

Cited by in corpus (11)

• T-duality in Massive Integrable Field Theories: The Homogeneous and Complex sine-Gordon Models
• T-dualization in a curved background in absence of a global symmetry
• Pseudoduality and Conserved Currents in Sigma Models
• Pseudoduality Between Symmetric Space Sigma Models
• Pseudoduality in Supersymmetric Sigma Models
• On the Hamiltonian formulation, integrability and algebraic structures of the Rajeev-Ranken model
• Euclidean Pseudoduality and Boundary Conditions in Sigma Models
• Pseudoduality in Supersymmetric Sigma Models on Symmetric Spaces
• Pseudoduality and Complex Geometry in Sigma Models
• Target Space Duality: The Dilaton Field
• Target Space Duality III: Potentials