(Non)-supersymmetric Marginal Deformations from Twistor String Theory

TL;DR

This paper explores how twistor string theory can be used to compute tree-level amplitudes in various marginally deformed gauge theories, including supersymmetric and non-supersymmetric cases, and proposes a consistent all-orders deformation framework.

Contribution

It extends twistor string theory methods to include all orders of marginal deformations, providing a unified approach for supersymmetric and non-supersymmetric theories.

Findings

Correctly reproduces tree-level amplitudes to first order in deformation parameter

Proposes an all-orders deformation framework matching field theory results

Shows equivalence of connected and disconnected instanton prescriptions in deformed theories

Abstract

The tree-level amplitudes in $\beta$-deformed theory are studied from twistor string theory. We first show that a simple generalization of the proposal in hep-th/0410122 gives the correct results for all of the tree-level amplitudes to the first order of the deformation parameter $\beta$. Then we give a proposal to all orders of $\beta$ and show this matches the field theory. We also show the prescription using connected instantons and the prescription using disconnected instantons are equivalent in the deformed twistor string theory. The tree-level amplitudes in non-supersymmetric $\gamma$-deformed theory are also obtained in this framework. The tree-level purely gluonic amplitudes in theories with generic marginal deformations are also discussed in the twistor string theory side.