Beta-deformation in Twistor-String Theory

TL;DR

This paper explores how the beta deformation of N=4 super-Yang-Mills theory appears within the topological B-model in twistor space, identifying the deformation's algebraic and cohomological structure and formulating the deformed action.

Contribution

It provides a detailed analysis of the beta deformation in twistor-string theory, including its representation, cohomology, and the explicit form of the deformed topological action.

Findings

Identified the beta deformation as a specific superconformal algebra state.

Computed the relevant BRST cohomology elements in the topological model.

Constructed the deformed topological action and BRST operator.

Abstract

In this work, we investigate how the marginal beta deformation of the ${N}=4$ super-Yang-Mills theory manifests within the context of the topological B-model in the twistor space $\mathbb{CP}^{3|4}$. We begin by identifying the beta deformation as states living in a specific irreducible representation of the superconformal algebra. Then, we compute the ghost number two elements of the BRST cohomology of the topological model. A gauge-fixing procedure is applied to these states, allowing us to identify the elements living in the irreducible representation that characterizes the beta deformation. Based on this identification, we proceed to write the deformed topological action, and the corresponding deformed BRST operator.