A Dual Description of the Four Dimensional Non-Linear Sigma Model

TL;DR

This paper constructs a dual formulation of the four-dimensional non-linear sigma model using string theory techniques, introduces a rank two antisymmetric tensor, and compares the physics of the dual and original models, confirming their equivalence at one loop.

Contribution

It provides a novel dual description of the four-dimensional non-linear sigma model, including the role of an antisymmetric tensor field, and verifies their equivalence through scattering amplitude analysis.

Findings

Dual model constructed with antisymmetric tensor field

Scattering amplitudes match at one loop for SU(2) chiral model

Dual and original theories are physically equivalent at this level

Abstract

The dual of the four dimensional non-linear sigma model is constructed using techniques familiar to string theory. This construction necessitates the introduction of a rank two antisymmetric tensor field whose properties are examined. The physics of the dual theory and that of the original model are compared. As an illustration we study in detail the SU(2) chiral model. We find that the scattering amplitudes of the charged Goldstone bosons in the two theories are in complete agreement at the one loop level.