Cubic Twistorial String Field Theory

TL;DR

This work constructs a cubic open string field theory action for Berkovits' twistorial string, introducing two cubic vertices of degree zero and one that uses a spectral-flow operator to raise degree. The action is shown to be gauge-invariant and parity-symmetric, with on-shell and off-shell analyses indicating correct cubic YM interactions and consistency with the first-quantized disk amplitude prescription. The parity mechanism is elucidated via Z^I–Y_I exchange, linking MHV and googly amplitudes and clarifying how the twistor formulation yields unitary N=4 SYM tree amplitudes. The framework offers a promising bridge between twistor-string ideas and conventional YM amplitudes, with potential extensions to loops and nonperturbative regimes.

Abstract

Witten has recently proposed a string theory in twistor space whose D-instanton contributions are conjectured to compute N=4 super-Yang-Mills scattering amplitudes. An alternative string theory in twistor space was then proposed whose open string tree amplitudes reproduce the D-instanton computations of maximal degree in Witten's model. In this paper, a cubic open string field theory action is constructed for this alternative string in twistor space, and is shown to be invariant under parity transformations which exchange MHV and googly amplitudes. Since the string field theory action is gauge-invariant and reproduces the correct cubic super-Yang-Mills interactions, it provides strong support for the conjecture that the string theory correctly computes N-point super-Yang-Mills tree amplitudes.