Color/kinematics duality for general abelian orbifolds of N=4 super Yang-Mills theory

Abstract

To explore color/kinematics duality for general representations of the gauge group we formulate the duality for general abelian orbifolds of the SU(N), N=4 super Yang-Mills theory in four dimensions, which have fields in the bi-fundamental representation, and use it to construct explicitly complete four-vector and four-scalar amplitudes at one loop. For fixed number of supercharges, graph-organized L-loop n-point integrands of all orbifold theories are given in terms of a fixed set of polynomials labeled by L representations of the orbifold group. In contrast to the standard duality-satisfying presentation of amplitudes of the N=4 super Yang-Mills theory, each graph may appear several times with different internal states. The color and R-charge flow provide a way to deform the amplitudes of orbifold theories to those of more general quiver gauge theories which do not necessarily exhibit color/kinematics duality on their own. Based on the organization of amplitudes required by the duality between color and kinematics in orbifold theories we show how the amplitudes of certain non-factorized matter-coupled supergravity theories can be found through a double-copy construction. We also carry out a comprehensive search for theories with fields solely in the adjoint representation of the gauge group and amplitudes exhibiting color/kinematics duality for all external states and find an interesting relation between supersymmetry and existence of the duality.

51 pages, 7 figures, PDFLaTex, typos fixed, minor changes in section 3.2

References in corpus (10)

• New Relations for Gauge-Theory Amplitudes
• 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
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• BCJ duality and double copy in the closed string sector

Cited by in corpus (66)

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• The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order
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• On the Double Copy for Spinning Matter
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Gauged supergravities and spontaneous SUSY breaking from the double copy
• Monopoles, shockwaves and the classical double copy
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• Constraints on a Massive Double-Copy and Applications to Massive Gravity
• Scattering equations and virtuous kinematic numerators and dual-trace functions
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• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Double copy for Lagrangians at trilinear order
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• Double-copy towards supergravity inflation with $\alpha$-attractor models
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• Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies
• Non-Abelian gauged supergravities as double copies
• Next-to-MHV Yang-Mills kinematic algebra
• The Weyl double copy from twistor space
• BCJ Amplitude Relations for Anti-de Sitter Boundary Correlators in Embedding Space
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
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• CHY Theory for Several Fields
• Relations and representations of QCD amplitudes
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• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity
• On-Shell Perspectives on the Massless Limit of Massive Supergravity