Virtues of a symmetric-structure double copy

Abstract

We demonstrate a physical motivation for extending color-dual or BCJ double-copy construction to include theories with kinematic numerators that obey the same algebraic relations as symmetric structure constants, $d^{abc}=\text{Tr}[\{T^a,T^b\}{T}^c]$. We verify that $U(N_c)$ nonlinear sigma model (NLSM) pions, long known to be color-dual in terms of antisymmetric adjoint factors, $f^{abc}$, are also color-dual in the sense of symmetric color structures, $d^{abc}$, explicitly through six-point scattering. This reframing of NLSM pion amplitudes complements our compositional construction of $d^{abc}$ color-dual higher derivative gauge operators. With adjoint and symmetric color-dual kinematics, we can span all four-point effective photon operators via a double-copy construction using amplitudes from physical theories. We further comment on a tension between locality and adjoint effective numerators, and the implications for spanning gravitational effective operators with non-adjoint kinematics.

v2: Matches version accepted for publication. v1: 8 pages

References in corpus (18)

• New Relations for Gauge-Theory Amplitudes
• The Effective Field Theory of Inflation
• The Effective Field Theory of Cosmological Large Scale Structures
• Effective Field Theory for Inflation
• Starting the Universe: Stable Violation of the Null Energy Condition and Non-standard Cosmologies
• Power-counting and the Validity of the Classical Approximation During Inflation
• The EFT-Hedron
• Sharp Boundaries for the Swampland
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• Hilbert Series for Constructing Lagrangians: expanding the phenomenologist's toolbox
• Two-Loop Renormalization of Quantum Gravity Simplified
• Composing Effective Prediction at Five Points
• Curvature-Squared Multiplets, Evanescent Effects and the U(1) Anomaly in N = 4 Supergravity
• Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons
• Double-copy towards supergravity inflation with $\alpha$-attractor models
• A tale of tails through generalized unitarity
• Electromagnetic Duality and D3-Brane Scattering Amplitudes Beyond Leading Order
• Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes

Cited by in corpus (4)

• Effective observables for electromagnetic duality from novel amplitude decomposition
• Color-Kinematic Numerators for Fermion Compton Amplitudes
• $D$-Dimensional Modular Assembly of Higher-Derivative Four-Point Contact Amplitudes Involving Fermions
• Entire Four-Graviton EFT from the Duality Between Color and Kinematics