N=2,4 Supersymmetric Gauge Field Theory in 2T-physics

TL;DR

This paper constructs the most general N=2 and N=4 supersymmetric Yang-Mills theories within 2T-physics in 4+2 dimensions, extending previous N=1 work, and explores their reductions to 3+1 dimensions revealing dualities and potential for non-perturbative solutions.

Contribution

It introduces the complete formulation of N=2 and N=4 supersymmetric gauge theories in 2T-physics, including actions, currents, and transformation laws, and connects them to known 3+1 dimensional theories.

Findings

Constructed N=2,4 supersymmetric Yang-Mills theories in 4+2 dimensions.

Derived shadows in 3+1 dimensions that match known supersymmetric theories.

Showed dualities between different 3+1 dimensional shadows.

Abstract

In the context of Two Time Physics in 4+2 dimensions we construct the most general N=2,4 supersymmetric Yang Mills gauge theories for any gauge group G. This builds on our previous work for N=1 supersymmetry. The action, the conserved SUSY currents, and the off-shell SU(N) covariant SUSY transformation laws are presented for both N=2 and N=4. The on-shell SUSY transformations close to the supergroup SU(2,2$|$N) with N=1,2,4. The SU(2,2)=SO(4,2) sub-symmetry is realized linearly on 4+2 dimensional flat spacetime. All fields, including vectors and spinors, are in 4+2 dimensions. The extra gauge symmetries in 2T field theory, together with the kinematic constraints that follow from the action, remove all the ghosts to give a unitary theory. By choosing gauges and solving the kinematic equations, the 2T field theory in 4+2 flat spacetime can be reduced to various shadows in various 3+1 dimensional (generally curved) spacetimes. These shadows are related to each other by dualities. The conformal shadows of our theories in flat 3+1 dimensions coincide with the well known counterpart N=1,2,4 supersymmetric massless renormalizable field theories in 3+1 dimensions. It is expected that our more symmetric new structures in 4+2 spacetime may be useful for non-perturbative or exact solutions of these theories.