Gauge Symmetries of the N=2 String

TL;DR

This paper analyzes the gauge symmetry algebra of the N=2 string, revealing it as a volume-preserving diffeomorphism algebra of the target torus, and presents a background-independent spacetime action with these symmetries.

Contribution

It identifies the unbroken gauge symmetries of the N=2 string as a volume-preserving diffeomorphism algebra of the target torus and constructs a background-independent spacetime action.

Findings

Unbroken gauge symmetries form a volume-preserving diffeomorphism algebra.

The ground ring of functions on the torus is acted upon by these symmetries as derivations.

A background-independent spacetime action with volume-preserving diffeomorphism symmetry is proposed.

Abstract

We study the underlying gauge symmetry algebra of the $N=2$ string, which is broken down to a subalgebra in any spacetime background. For given toroidal backgrounds, the unbroken gauge symmetries (corresponding to holomorphic and antiholomorphic worldsheet currents) generate area-preserving diffeomorphism algebras of null 2-tori. A minimal Lie algebraic closure containing all the gauge symmetries that arise in this way, is the background--independent volume--preserving diffeomorphism algebra of the target Narain torus $T^{4,4}$. The underlying symmetries act on the ground ring of functions on $T^{4,4}$ as derivations, much as in the case of the $d=2$ string. A background--independent spacetime action valid for noncompact metrics is presented, whose symmetries are volume--preserving diffeomorphisms. Possible extensions to $N=2$ and $N=1$ heterotic strings are briefly discussed.