N=2 strings and the twistorial Calabi-Yau

TL;DR

The paper proposes a twistorial string framework in which A- and B-model topological strings on $\mathbf{CP}^{3|4}$ serve as dual descriptions of open $N=2$ string theory in a (2,2) spacetime, with D1-instantons ending on $\mathbf{RP}^{3|4}$ branes deforming self-dual ${\mathcal N}=4$ YM to full YM. It argues for an S-duality between the A- and B-model realizations and invokes mirror symmetry to explain the twistor-space localization of amplitudes, including a conjectured mirror to a quadric in $\mathbf{CP}^{3|3} \times \mathbf{CP}^{3|3}$. Central to the construction are speculative NS2-branes on $\mathbf{RP}^{3|4}$ and NS5-branes that cancel tadpoles and enable dual descriptions, potentially tying together twistorial YM with holomorphic CS on mirror geometries. If borne out, the program offers a geometric, string-theoretic derivation of four-dimensional YM amplitudes from topological strings, extending the twistor approach beyond the planar limit.

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.