N=2 strings and the twistorial Calabi-Yau

TL;DR

This paper explores the relationship between topological string theories on supertwistor space and N=2 string theory, proposing dualities, instanton effects, and mirror symmetry explanations for N=4 Yang-Mills amplitudes.

Contribution

It introduces a novel interpretation of topological strings as N=2 strings and proposes dualities and instanton effects that deform self-dual Yang-Mills to full Yang-Mills.

Findings

Topological strings on CP^{3|4} relate to open N=2 string theory.

Instantons on Lagrangian branes deform self-dual to full Yang-Mills.

Mirror symmetry may explain twistor space amplitude structures.

Abstract

We interpret the A and B model topological strings on CP^{3|4} as equivalent to open N=2 string theory on spacetime with signature (2,2), when covariantized with respect to SO(2,2) and supersymmetrized a la Siegel. We propose that instantons ending on Lagrangian branes wrapping RP^{3|4} deform the self-dual N=4 Yang-Mills sector to ordinary Yang-Mills by generating a `t Hooft like expansion. We conjecture that the A and B versions are S-dual to each other. We also conjecture that mirror symmetry may explain the recent observations of Witten that twistor transformed N=4 Yang-Mills amplitudes lie on holomorphic curves.