Cubic Twistorial String Field Theory

TL;DR

This paper constructs a cubic open string field theory in twistor space that is gauge-invariant, reproduces super-Yang-Mills interactions, and supports the conjecture that it computes N-point tree amplitudes.

Contribution

It introduces a new cubic string field theory in twistor space that is parity-invariant and aligns with super-Yang-Mills amplitude computations, advancing the twistor string framework.

Findings

String field theory action is gauge-invariant.

Reproduces correct super-Yang-Mills cubic interactions.

Supports the conjecture of computing N-point tree amplitudes.

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.