Marginal Deformations of N=4 SYM from Open/Closed Twistor Strings

TL;DR

This paper explores how marginal deformations of N=4 SYM can be understood through open/closed twistor string theory, revealing a non-anticommutative structure and extending the twistor formalism for N=1 theories.

Contribution

It demonstrates how to realize N=4 SYM deformations in twistor string theory via closed string backgrounds and extends the twistor formalism to N=1 theories with a star product.

Findings

Deformation corresponds to non-anticommutativity in supertwistor space.

The extended twistor formalism reproduces expected results at linear order.

The approach links gauge theory deformations with string theory backgrounds.

Abstract

We investigate how the marginal deformations of N=4 supersymmetric Yang-Mills theory (analysed in particular by Leigh and Strassler) arise within B-model topological string theory on supertwistor space CP(3|4). This is achieved by turning on a certain closed string background in the fermionic directions. Through a specific open/closed correlation function, this mode induces a correction to holomorphic Chern-Simons theory, corresponding to the self-dual part of the chiral operator added on the gauge theory side. The effect of the deformation is interpreted as non-anticommutativity between some of the odd coordinates of CP(3|4). Motivated by this, we extend the twistor formalism for calculating MHV amplitudes in N=4 SYM to these N=1 theories by introducing a suitable star product between the wavefunctions. We check that our prescription yields the expected results to linear order in the deformation parameter.