Gauge and Gravity Amplitude Relations

Abstract

In these lectures I talk about simplifications and universalities found in scattering amplitudes for gauge and gravity theories. In contrast to Ward identities, which are understood to arise from familiar symmetries of the classical action, these structures are currently only understood in terms of graphical organizational principles, such as the gauge-theoretic color-kinematics duality and the gravitational double-copy structure, for local representations of multi-loop S-matrix elements. These graphical principles make manifest new relationships in and between gauge and gravity scattering amplitudes. My lectures will focus on arriving at such graphical organizations for generic theories with examples presented from maximal supersymmetry, and their use in unitarity-based multi-loop integrand construction.

Presented at the Theoretical Advanced Study Institute (TASI 2014), Boulder, CO, June 2-27, 2014

References in corpus (21)

• New Relations for Gauge-Theory Amplitudes
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Minimal Basis for Gauge Theory Amplitudes
• Black holes and the double copy
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Amplitudes and Spinor-Helicity in Six Dimensions
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• Yang-Mills origin of gravitational symmetries
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Gravity and Yang-Mills Amplitude Relations
• Positive Amplitudes In The Amplituhedron
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
• KLT relations from the Einstein-Hilbert Lagrangian
• Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
• Fundamental BCJ Relation in N=4 SYM From The Connected Formulation
• Amplitudes at Weak Coupling as Polytopes in AdS_5
• Cohomology foundations of one-loop amplitudes in pure spinor superspace
• MHV Lagrangian for N=4 Super Yang-Mills
• The Ultraviolet Critical Dimension of Half-Maximal Supergravity at Three Loops

Cited by in corpus (26)

• The Effective Field Theorist's Approach to Gravitational Dynamics
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• The classical double copy for Taub-NUT spacetime
• The Kerr-Schild double copy in curved spacetime
• Screw-symmetric gravitational waves: a double copy of the vortex
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• Standard Model Theory for the FCC-ee Tera-Z stage
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
• The SU(2|3) dynamic two-loop form factors
• Off-shell Currents and Color-Kinematics Duality
• More on the Classical Double Copy in Three Spacetime Dimensions
• Full-color three-loop three-point form factors in N=4 SYM
• Classical Double Copy of Spinning Worldline Quantum Field Theory
• Double-Copying Self-Dual Yang-Mills Theory to Self-Dual Gravity on Twistor Space
• Pair Production and Gravity as the Weakest Force
• The classical double copy in curved spacetimes: Perturbative Yang-Mills from the bi-adjoint scalar
• Loop-level double-copy for massive fermions in the fundamental
• BCJ, worldsheet quantum algebra and KZ equations
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals
• The double copy effective action: a quantum (chromodynamics) approach to space-time
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• Field theory for gravity at all scales
• On-shell Methods for Form Factors in N=4 SYM and Their Applications
• Energy Flow in Particle Collisions
• Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations