Abstract

The tree-level amplitudes in the β-deformed supersymmetric gauge theory are derived from twistor string theory. We first show that a simple generalization of [M. Kulaxizi, K. Zoubos, Marginal deformations of N = 4 SYM from open/closed twistor strings, Nucl. Phys. B 738 (2006) 317, hep-th/0410122] gives us the desired results for all the tree-level amplitudes up to first order in the deformation parameter β. Then we provide a new proposal which matches field theory to all orders of β. With our deformed twistor string theory, it can be shown that integration over connected instantons and disconnected instantons remain equivalent. The tree-level amplitudes in the non-supersymmetric γ-deformed theory can be obtained using a similar deformation of the twistor string. Finally, we find improved twistor string results for the tree-level purely gluonic amplitudes in theories with more general marginal deformations.

Highlights

  • One of the important issues in AdS/CFT correspondence [1, 2, 3] is to study the closed string dual of the gauge theories with less supersymmtries

  • We propose an all-order exact prescription for the non-anti-commutative star product and show that this new prescription gives the right complete field theory results

  • In the expression corresponding to the MHV diagram, for every vertex, these factors from the propagators connected to it and the wavefunctions of the external particles connected to it should be multiplied using the star product in supertwistor space to give the amplitudes in β-deformed theory

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Summary

Introduction

One of the important issues in AdS/CFT correspondence [1, 2, 3] is to study the closed string dual of the gauge theories with less supersymmtries. A prescription for calculating the tree-level amplitudes in the deformed theory using the connected instantons was proposed in that paper and shown to produce desired field theory results to the first order of the deformation parameter. In this prescription, a non-anti-commutative star product among the wavefunctions of the external particles plays an important role. We give an prescription to all orders of γ to reproduce tree-level field theory amplitudes from the deformed twistor string theory Encouraged by these success, we proceed to find some further evidence for a possible all-degree closed form answer for theories with generic LeighStrassler deformations. The final section is devoted to conclusions and directions for further studies

Review of tree-level Yang-Mills amplitudes
Amplitudes in deformed SYM from twistor strings
All tree-level amplitudes to linear order in β
The star product to all orders of β
Pure gluonic amplitudes in the general deformed theory
I3K1 I3 K 1
Conclusion and discussions
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