Supersymmetric Field Theory in 2T-physics

TL;DR

This paper develops N=1 supersymmetry within 2T-physics in 4+2 dimensions, deriving 3+1 dimensional supersymmetric theories with unique constraints and potential implications for cosmology and non-perturbative physics.

Contribution

It constructs a consistent N=1 supersymmetric field theory in 4+2 dimensions compatible with 2T-physics, revealing novel restrictions and dualities in emergent 3+1 theories.

Findings

Emergent 3+1 SUSY theories lack CP-violating F*F terms.

Superpotential has no dimensionful parameters.

4+2 structure constrains 3+1 SUSY field theory.

Abstract

We construct N=1 supersymmetry in 4+2 dimensions compatible with the theoretical framework of 2T physics field theory and its gauge symmetries. The fields are arranged into 4+2 dimensional chiral and vector supermultiplets, and their interactions are uniquely fixed by SUSY and 2T-physics gauge symmetries. Many 3+1 spacetimes emerge from 4+2 by gauge fixing. Gauge degrees of freedom are eliminated as one comes down from 4+2 to 3+1 dimensions without any remnants of Kaluza-Klein modes. In a special gauge, the remaining physical degrees of freedom, and their interactions, coincide with ordinary N=1 supersymmetric field theory in 3+1 dimensions. In this gauge, SUSY in 4+2 is interpreted as superconformal symmetry SU(2,2|1) in 3+1 dimensions. Furthermore, the underlying 4+2 structure imposes some interesting restrictions on the emergent 3+1 SUSY field theory, which could be considered as part of the predictions of 2T-physics. One of these is the absence of the troublesome renormalizable CP violating F*F terms. This is good for curing the strong CP violation problem of QCD. An additional feature is that the superpotential is required to have no dimensionful parameters. To induce phase transitions, such as SUSY or electro-weak symmetry breaking, a coupling to the dilaton is needed. This suggests a common origin of phase transitions that is driven by the vacuum value of the dilaton, and need to be understood in a cosmological scenario as part of a unified theory that includes the coupling of supergravity to matter. Another interesting aspect is the possibility to utilize the inherent 2T gauge symmetry to explore dual versions of the N=1 theory in 3+1 dimensions. This is expected to reveal non-perturbative aspects of ordinary 1T field theory.