The target space geometry of N=(2,1) string theory

TL;DR

This paper investigates the geometric constraints on the target space of the N=(2,1) heterotic superstring imposed by supersymmetry and currents, revealing a connection to a 2+2-dimensional object in a 10+2-dimensional spacetime with null isometry.

Contribution

It derives the ${ m O}( extstyle{rac{ extstyle{ m alpha'}^0})}$ constraints on target space geometry considering quantum effects and interprets the geometry in terms of a higher-dimensional object in a spacetime with null isometry.

Findings

Constraints on target space geometry from supersymmetry and currents.

Quantum effects influence the geometric constraints at tree and one-loop levels.

Interpretation of the geometry as a 2+2-dimensional object in 10+2 spacetime with null isometry.

Abstract

We describe the ${\cal{O}}({\alpha'}^0)$ constraints on the target space geometry of the $N=(2,1)$ heterotic superstring due to the left-moving $N=1$ supersymmetry and $U(1)$ currents. In the fermionic description of the internal sector supersymmetry is realized quantum mechanically, so that both tree-level and one-loop effects contribute to the order ${\cal{O}}({\alpha'}^0)$ constraints. We also discuss the physical interpretation of the resulting target space geometry in terms of configurations of a $2+2$-dimensional object propagating in a $10+2$-dimensional spacetime with a null isometry, which has recently been suggested as a unified description of string and M theory.