On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes

Abstract

We define a perturbatively calculable quantity--the on-shell correlator--which furnishes a unified description of particle dynamics in curved spacetime. Specializing to the case of flat and anti-de Sitter space, on-shell correlators coincide precisely with on-shell scattering amplitudes and boundary correlators, respectively. Remarkably, we find that symmetric manifolds admit a generalization of on-shell kinematics in which the corresponding momenta are literally the isometry generators of the spacetime acting on the external kinematic data. These isometric momenta are intrinsically non-commutative but exhibit on-shell conditions that are identical to those of flat space, thus providing a common language for computing and representing on-shell correlators which is agnostic about the underlying geometry. Afterwards, we compute tree-level on-shell correlators for biadjoint scalar (BAS) theory and the nonlinear sigma model (NLSM) and learn that color-kinematics duality is manifested at the level of fields under a mapping of the color algebra to the algebra of gauged isometries on the spacetime manifold. Last but not least, we present a field theoretic derivation of the fundamental BCJ relations for on-shell correlators following from the existence of certain conserved currents in BAS theory and the NLSM.

arXiv comment42 pages + refs

References in corpus (80)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• New Relations for Gauge-Theory Amplitudes
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Gluon scattering amplitudes at strong coupling
• Perturbative Quantum Gravity as a Double Copy of Gauge Theory
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• The Amplituhedron
• Writing CFT correlation functions as AdS scattering amplitudes
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• One-Loop Amplitudes for e^+ e^- to Four Partons
• Amplitudes, Observables, and Classical Scattering
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• New Color Decompositions for Gauge Amplitudes at Tree and Loop Level
• Massive Loop Amplitudes from Unitarity
• A Natural Language for AdS/CFT Correlators
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Spinning AdS Propagators
• Effective Field Theories from Soft Limits
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Unitarity and the Holographic S-Matrix
• Mellin amplitudes for $Ad{S}_5\times S^5$
• Towards Feynman rules for Mellin amplitudes in AdS/CFT
• Bootstrapping Inflationary Correlators in Mellin Space
• How to Succeed at Holographic Correlators Without Really Trying
• The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds
• Gravitational S-matrix from CFT dispersion relations
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• The Ultraviolet Properties of N=4 Supergravity at Four Loops
• Gravitational Bremsstrahlung from Reverse Unitarity
• A Mellin Space Approach to Cosmological Correlators
• The Cosmological Optical Theorem
• Analyticity and Unitarity for Cosmological Correlators
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• The boundary S-matrix and the AdS to CFT dictionary
• Cosmological Cutting Rules
• Weight Shifting Operators and Conformal Blocks
• Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
• $d$-dimensional SYK, AdS Loops, and $6j$ Symbols
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• A first look at two-loop five-gluon scattering in QCD
• Cutting Cosmological Correlators
• From Locality and Unitarity to Cosmological Correlators
• What Do CFTs Tell Us About Anti-de Sitter Spacetimes?
• A Hidden Symmetry of the Galileon
• Double copy structure of CFT correlators
• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• Renormalised 3-point functions of stress tensors and conserved currents in CFT
• Gluon Scattering in AdS from CFT
• The Inflationary Wavefunction from Analyticity and Factorization
• On duality of color and kinematics in (A)dS momentum space
• TASI lectures on AdS/CFT
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• Color/Kinematics Duality in AdS${}_4$
• BCFW for Witten Diagrams
• Spinning AdS Loop Diagrams: Two Point Functions
• Unitarity Methods in AdS/CFT
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• CFT Unitarity and the AdS Cutkosky Rules
• Double copy structure and the flat space limit of conformal correlators in even dimensions
• Double Copy Relation for AdS
• Geometric Soft Theorems
• Shift Symmetries in (Anti) de Sitter Space
• An étude of momentum space scalar amplitudes in AdS
• Holographic dual of the five-point conformal block
• Double copy structure of parity-violating CFT correlators
• Scattering Equations in AdS: Scalar Correlators in Arbitrary Dimensions
• AdS Weight Shifting Operators
• A Differential Representation of Cosmological Wavefunctions
• From bulk loops to boundary large-N expansion
• A multipoint conformal block chain in $d$ dimensions
• Towards Color-Kinematics Duality in Generic Spacetimes
• Dispersion Formulas in QFTs, CFTs, and Holography
• Amplitudes at Infinity
• UV cancelations in gravity loop integrands
• Manifesting enhanced cancellations in supergravity: integrands versus integrals
• Gravity loop integrands from the ultraviolet