Einstein Supergravity and New Twistor String Theories

TL;DR

This paper constructs new twistor string theories that produce Einstein supergravity spectra with second order equations, avoiding higher derivative issues of earlier models, and verifies their consistency through amplitude calculations.

Contribution

It introduces a family of anomaly-free twistor string theories that yield Einstein supergravity spectra, including N=8 and N=4 supergravities, with explicit amplitude computations.

Findings

Theories are free from world-sheet anomalies.

Spectra correspond to Einstein supergravities with second order equations.

Calculated three-graviton amplitudes match Einstein supergravity interactions.

Abstract

A family of new twistor string theories is constructed and shown to be free from world-sheet anomalies. The spectra in space-time are calculated and shown to give Einstein supergravities with second order field equations instead of the higher derivative conformal supergravities that arose from earlier twistor strings. The theories include one with the spectrum of N=8 supergravity, another with the spectrum of N=4 supergravity coupled to N=4 super-Yang-Mills, and a family with $N\ge 0$ supersymmetries with the spectra of self-dual supergravity coupled to self-dual super-Yang-Mills. The non-supersymmetric string with N=0 gives self-dual gravity coupled to self-dual Yang-Mills and a scalar. A three-graviton amplitude is calculated for the N=8 and N=4 theories and shown to give a result consistent with the cubic interaction of Einstein supergravity.