N=1 Super-$\tau_{3}$QED from Atiyah-Ward Space-Time

TL;DR

This paper derives a supersymmetric extension of super-QED in (1+2) dimensions via dimensional reduction from a (2+2)-dimensional theory, highlighting the role of chiral superfields and specific truncations.

Contribution

It constructs the massive super-{ au}_{3}QED in (1+2) dimensions from a higher-dimensional theory using Scherk reduction, revealing new supersymmetric structures.

Findings

Derived the action for massive super-{ au}_{3}QED.

Performed dimensional reduction from (2+2) to (1+2) dimensions.

Showed supersymmetric extension emerges after truncations.

Abstract

In this letter, we present the action for the massive super-{\QED}. A pair of chiral and a pair of anti-chiral superfields with opposite U(1)-charges are required. We also carry out a dimensional reduction {\it{\`a la}} Scherk from (2+2) to (1+2) dimensions, and we show that, after suitable truncations are performed, the supersymmetric extension of the ${\tau}_{3}$QED$_{1+2}$ naturally comes out.