Sigma Models with N=8 Supersymmetries in 2+1 and 1+1 Dimensions

TL;DR

This paper develops an N=8 supersymmetric extension of a Yang-Mills-Higgs model in 2+1 dimensions, relating it to a chiral model with a Wess-Zumino-Witten term, and further reduces it to 1+1 dimensions for sigma models.

Contribution

It introduces a novel N=8 supersymmetric model in 2+1 dimensions and connects it to known chiral and Grassmannian sigma models through dimensional reduction.

Findings

Establishes equivalence between the supersymmetric Yang-Mills-Higgs model and a chiral model with Wess-Zumino-Witten term.

Derives N=(8,8) supersymmetric extensions of standard U(n) chiral and Grassmannian sigma models.

Provides a framework linking twistor string theory with supersymmetric sigma models.

Abstract

We introduce an N=8 supersymmetric extension of the Bogomolny-type model for Yang-Mills-Higgs fields in 2+1 dimensions related with twistor string theory. It is shown that this model is equivalent to an N=8 supersymmetric U(n) chiral model in 2+1 dimensions with a Wess-Zumino-Witten-type term. Further reduction to 1+1 dimensions yields N=(8,8) supersymmetric extensions of the standard U(n) chiral model and Grassmannian sigma models.