Triality Invariance in the N=2 Superstring

TL;DR

This paper proves the triality invariance of the N=2 superstring in a 2+2 dimensional space, extending it to different formulations and introducing a supersymmetric hyperdeterminant based on superalgebra invariants.

Contribution

It demonstrates the triality invariance in the N=2 superstring and introduces a supersymmetric hyperdeterminant related to superalgebra invariants.

Findings

Triality invariance in N=2 superstring proven

Invariance extends to Siegel-Berkovits formulation

Supersymmetric hyperdeterminant based on superalgebra introduced

Abstract

We prove the discrete triality invariance of the N=2 NSR superstring moving in a D=2+2 target space. We find that triality holds also in the Siegel-Berkovits formulation of the selfdual superstring. A supersymmetric generalization of Cayley's hyperdeterminant, based on a quartic invariant of the SL(2|1)^3 superalgebra, is presented.