Space-Time Supersymmetry of Extended Fermionic Strings in $2 + 2$ Dimensions

TL;DR

This paper explores the space-time supersymmetry and Lorentz covariance of extended fermionic strings in 2+2 dimensions, proposing an equivalence to a local quantum supersymmetric field theory and discussing implications for string symmetries and spectrum.

Contribution

It demonstrates the equivalence of N=2 and N=4 fermionic string models and analyzes their space-time symmetries and spectrum in 2+2 dimensions, emphasizing supersymmetry and Lorentz invariance.

Findings

Presence of SO(2,2) Lorentz symmetry in the theory

Existence of at least one self-dual space-time supersymmetry

Absence of massive string modes and vanishing loop amplitudes

Abstract

The $N=2$ fermionic string theory is revisited in light of its recently proposed equivalence to the non-compact $N=4$ fermionic string model. The issues of space-time Lorentz covariance and supersymmetry for the BRST quantized $N=2$ strings living in uncompactified $2 + 2$ dimensions are discussed. The equivalent local quantum supersymmetric field theory appears to be the most transparent way to represent the space-time symmetries of the extended fermionic strings and their interactions. Our considerations support the Siegel's ideas about the presence of $SO(2,2)$ Lorentz symmetry as well as at least one self-dual space-time supersymmetry in the theory of the $N=2(4)$ fermionic strings, though we do not have a compelling reason to argue about the necessity of the {\it maximal} space-time supersymmetry. The world-sheet arguments about the absence of all string massive modes in the physical spectrum, and the vanishing of all string-loop amplitudes in the Polyakov approach, are given on the basis of general consistency of the theory.