Closed N=2 Strings: Picture-Changing, Hidden Symmetries and SDG Hierarchy

TL;DR

This paper explores the symmetries and hierarchy structures in closed N=2 string theory, revealing connections to self-dual gravity and uncovering infinite symmetries that explain amplitude cancellations.

Contribution

It identifies the action of picture-changing and spectral flow operators on the ground ring, deriving the full symmetry hierarchy of self-dual gravity from N=2 string theory.

Findings

Infinite symmetry charges act on physical states.

Hierarchy of commuting flows on self-dual metrics.

Hidden abelian symmetries explain amplitude vanishing.

Abstract

We study the action of picture-changing and spectral flow operators on a ground ring of ghost number zero operators in the chiral BRST cohomology of the closed N=2 string and describe an infinite set of symmetry charges acting on physical states. The transformations of physical string states are compared with symmetries of self-dual gravity which is the effective field theory of the closed N=2 string. We derive all infinitesimal symmetries of the self-dual gravity equations in 2+2 dimensional spacetime and introduce an infinite hierarchy of commuting flows on the moduli space of self-dual metrics. The dependence on moduli parameters can be recovered by solving the equations of the SDG hierarchy associated with an infinite set of abelian symmetries generated recursively from translations. These non-local abelian symmetries are shown to coincide with the hidden abelian string symmetries responsible for the vanishing of most scattering amplitudes. Therefore, N=2 string theory "predicts" not only self-dual gravity but also the SDG hierarchy.