Twistors, strings and supersymmetric gauge theories

Abstract

This thesis is concerned with the study of scattering amplitudes in four-dimensional conformal field theories, more particularly the N=4 super-Yang-Mills theory. We study this theory first at tree level by using twistor space techniques and review the twistor string models that were proposed to describe it. Then, we turn to the issue of iteration relations and all loop ansatze for scattering amplitudes. We review the unitarity method for computing scattering amplitudes and discuss the Wilson loop--scattering amplitude duality that was inspired by the strong-coupling prescription of Alday and Maldacena for scattering amplitudes. We describe in some detail the computation of a two-loop six-point scattering amplitude and its surprising equality to the polygonal Wilson loop.

PhD thesis, 162 pages. Does not include discussion of and references to some recent work done after the submission of the thesis manuscript. v2 added reference, minor changes

References in corpus (73)

• Large N Field Theories, String Theory and Gravity
• Wilson loops in large N field theories
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
• New Relations for Gauge-Theory Amplitudes
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Gluon scattering amplitudes at strong coupling
• Cuba - a library for multidimensional numerical integration
• Multi-Parton Amplitudes in Gauge Theories
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• MHV Vertices And Tree Amplitudes In Gauge Theory
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• Magic identities for conformal four-point integrals
• Applied Conformal Field Theory
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Automatized analytic continuation of Mellin-Barnes integrals
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• On planar gluon amplitudes/Wilson loops duality
• Anti De Sitter Space And Holography
• Comments on gluon scattering amplitudes via AdS/CFT
• Hexagon Wilson loop = six-gluon MHV amplitude
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• On Tree Amplitudes in Gauge Theory and Gravity
• Three-Loop Superfiniteness of N=8 Supergravity
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• An Alternative String Theory in Twistor Space for N=4 Super-Yang-Mills
• Perturbative Quantum Gravity and its Relation to Gauge Theory
• The self-dual sector of QCD amplitudes
• All-Order Collinear Behavior in Gauge Theories
• The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Gauge Theory Amplitudes In Twistor Space And Holomorphic Anomaly
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Twistor Space Structure Of One-Loop Amplitudes In Gauge Theory
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• Unexpected Cancellations in Gravity Theories
• Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS_5 x S^5
• Sharpening The Leading Singularity
• The No-Triangle Hypothesis for N=8 Supergravity
• New Higher-Derivative $R^4$ Theorems
• Supersymmetry counterterms revisited
• Lectures on Twistor Strings and Perturbative Yang-Mills Theory
• Cubic Twistorial String Field Theory
• Self-Dual N=8 Supergravity as Closed N=2(4) Strings
• Introduction to AdS-CFT
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• A mini-course on topological strings
• Twistor Actions for Self-Dual Supergravities
• Simplifying Algebra in Feynman Graphs, Part II: Spinor Helicity from the Spacecone
• Untwisting the twistor superstring
• Infrared Limit of Gluon Amplitudes at Strong Coupling
• Implications of multi-Regge limits for the Bern-Dixon-Smirnov conjecture
• On the structure of scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity
• Tree and Loop Amplitudes in Open Twistor String Theory
• Planar quark scattering at strong coupling and universality
• Scattering amplitudes in strongly coupled N=4 SYM from semiclassical strings in AdS
• On collinear factorization of Wilson loops and MHV amplitudes in N=4 SYM
• Orbifolding the Twistor String
• Simplifying Algebra in Feynman Graphs, Part I:Spinors
• Equivalence of twistor prescriptions for super Yang-Mills
• On the Factorisation of the Connected Prescription for Yang-Mills Amplitudes
• Gluon scattering in $\mathcal{N}=4$ Super Yang-Mills at finite temperature
• A Note on Graviton Amplitudes for New Twistor String Theories
• Simplifying Algebra in Feynman Graphs, Part III: Massive Vectors
• Gluon Scattering in Deformed N=4 SYM
• $R^4$ terms in supergravity and M-theory
• One-loop N=8 Supergravity Amplitudes from MHV Diagrams
• (Non)-supersymmetric Marginal Deformations from Twistor String Theory
• Two-Loop N=4 Supersymmetric Amplitudes and QCD

Cited by in corpus (1)

• Conformal Supergravity Tree Amplitudes from Open Twistor String Theory