Extended Self-Dual Yang-Mills from the N=2 String

TL;DR

This paper demonstrates that the degrees of freedom of an N=2 string are described by a self-dual Yang-Mills theory on a hyperspace, introducing a tower of fields with an action for their interactions, including a truncation with no multi-loop graphs.

Contribution

It introduces a novel description of N=2 string degrees of freedom via self-dual Yang-Mills on hyperspace with an infinite tower of interacting fields.

Findings

The physical states are described by a self-dual Yang-Mills field on hyperspace.

An action for the infinite tower of fields is constructed.

A truncation yields a theory with no multi-loop graphs.

Abstract

We show that the physical degrees of freedom of the critical open string with N=2 superconformal symmetry on the worldsheet are described by a self-dual Yang-Mills field on a hyperspace parametrised by the coordinates of the target space R^{2,2} together with a commuting chiral spinor. A prepotential for the self-dual connection in the hyperspace generates the infinite tower of physical fields corresponding to the inequivalent pictures or spinor ghost vacua of this string. An action is presented for this tower, which describes consistent interactions amongst fields of arbitrarily high spin. An interesting truncation to a theory of five fields is seen to have no graphs of two or more loops.