Twistor actions for gauge theory and gravity

Abstract

This is a review of recent developments in the study of perturbative gauge theory and gravity using action functionals on twistor space. It is intended to provide a user-friendly introduction to twistor actions, geared towards researchers or graduate students interested in learning something about the utility, prospects, and shortcomings of this approach. For those already familiar with the twistor approach, it should provide a condensed overview of the literature as well as several novel results of potential interest. This work is based primarily upon the author's D.Phil. thesis. We first consider four-dimensional, maximally supersymmetric Yang-Mills theory as a gauge theory in twistor space. We focus on the perturbation theory associated to this action, which in an axial gauge leads to the MHV formalism. This allows us to efficiently compute scattering amplitudes at tree-level (and beyond) in twistor space. Other gauge theory observables such as local operators and null polygonal Wilson loops can also be formulated twistorially, leading to proofs for several correspondences between correlation functions and Wilson loops, as well as a recursive formula for computing mixed Wilson loop / local operator correlators. We then apply the twistor action approach to general relativity, using the on-shell equivalence between conformal and Einstein gravity. This can be extended to N=4 supersymmetry. The perturbation theory of the twistor action leads to formulae for the MHV amplitude with and without cosmological constant, yields a candidate for the Einstein twistor action, and induces a MHV formalism on twistor space. Appendices include discussion of super-connections and Coulomb branch regularization on twistor space.

178 pages, 30 figures. Review based on the author's D.Phil. thesis. v2: references added

References in corpus (38)

• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• Einstein Gravity from Conformal Gravity
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• Is N = 8 Supergravity Ultraviolet Finite?
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• From Twistor Actions to MHV Diagrams
• Gravity from Rational Curves
• Tree Level Recursion Relations In General Relativity
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• More supersymmetric Wilson loops
• Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
• On semiclassical computation of 3-point functions of closed string vertex operators in AdS_5 x S^5
• MHV Diagrams in Momentum Twistor Space
• Twistor Actions for Self-Dual Supergravities
• A simple formula for gravitational MHV amplitudes
• Conformal and Einstein gravity from twistor actions
• Twistor Strings for N=8 Supergravity
• Heterotic twistor-string theory
• Tree-Level Amplitudes in N=8 Supergravity
• From dlogs to dilogs; the super Yang-Mills MHV amplitude revisited
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• CSW rules for a massive scalar
• Conformal Supergravity Tree Amplitudes from Open Twistor String Theory
• Holomorphic Linking, Loop Equations and Scattering Amplitudes in Twistor Space
• S-duality in Twistor Space
• Self-Dual Supergravity and Twistor Theory
• A Direct Proof of BCFW Recursion for Twistor-Strings
• A Note on Graviton Amplitudes for New Twistor String Theories
• The Coulomb-branch S-matrix from massless amplitudes
• Weighted integral formulas on manifolds
• The supersymmetric Penrose transform in six dimensions
• On Closed Twistor String Theory

Cited by in corpus (14)

• Conformal and Einstein gravity from twistor actions
• Conformal higher spin scattering amplitudes from twistor space
• Composite Operators in the Twistor Formulation of $\mathcal{N}=4$ SYM Theory
• Twistor Constructions for Higher-spin Extensions of (Self-dual) Yang-Mills
• Gravity with a cosmological constant from rational curves
• Gluon scattering on self-dual radiative gauge fields
• A Twistorial Approach to Integrability in N=4 SYM
• Minitwistors and 3d Yang-Mills-Higgs theory
• Twistors and antipodes in de Sitter space
• Twistor fishnets
• Pure Connection Formulation, Twistors and the Chase for a Twistor Action for General Relativity
• Twistor action for general relativity
• Lectures on twistor theory
• Spectrum, Scattering Amplitudes, and String Field Theory of 4 Dimensional Twistor String