Relating Auxiliary Field Formulations in 4D and 2D Field Theories
Analysis
This paper explores the connections between different auxiliary field formulations used in four-dimensional non-linear electrodynamics and two-dimensional integrable sigma models. It clarifies how these formulations are related through Legendre transformations and field redefinitions, providing a unified understanding of how auxiliary fields generate new models while preserving key properties like duality invariance and integrability. The paper establishes correspondences between existing formalisms and develops new frameworks for deforming integrable models, contributing to a deeper understanding of these theoretical constructs.
Key Takeaways
- •Clarifies the relationship between different auxiliary field formulations in 4D and 2D field theories.
- •Shows how these formulations are governed by Legendre transformations and field redefinitions.
- •Establishes a correspondence between the Russo-Townsend and Ivanov-Zupnik formalisms.
- •Develops a new framework (μ-frame) for deforming integrable models in 2D.
- •Extends known families of integrable deformations.
“The paper establishes a correspondence between the auxiliary field model of Russo and Townsend and the Ivanov--Zupnik formalism in four-dimensional electrodynamics.”