All-loop group-theory constraints for color-ordered SU(N) gauge-theory amplitudes

Abstract

We derive constraints on the color-ordered amplitudes of the L-loop four-point function in SU(N) gauge theories that arise solely from the structure of the gauge group. These constraints generalize well-known group theory relations, such as U(1) decoupling identities, to all loop orders.

12 pages, no figures; v2: added references, minor corrections; v3: minor clarifications, published version

References in corpus (8)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
• New relations for scattering amplitudes in Yang-Mills theory at loop level
• One-loop SYM-supergravity relation for five-point amplitudes

Cited by in corpus (26)

• The Ultraviolet Structure of Half-Maximal Supergravity with Matter Multiplets at Two and Three Loops
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• The three-loop form factor in N=4 super Yang-Mills
• Four-gluon scattering at three loops, infrared structure and Regge limit
• Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
• Two-parton scattering in the high-energy limit
• Higher-loop amplitude monodromy relations in string and gauge theory
• All-loop infrared-divergent behavior of most-subleading-color gauge-theory amplitudes
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• Scattering equations and virtuous kinematic numerators and dual-trace functions
• SU(N) group-theory constraints on color-ordered five-point amplitudes at all loop orders
• On powercounting in perturbative quantum gravity theories through color-kinematic duality
• Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts
• Full Colour for Loop Amplitudes in Yang-Mills Theory
• Color Dressed Unitarity and Recursion for Yang-Mills Two-Loop All-Plus Amplitudes
• On General BCJ Relation at One-loop Level in Yang-Mills Theory
• Linear relations between N >= 4 supergravity and subleading-color SYM amplitudes
• A minimal approach to the scattering of physical massless bosons
• Four-particle scattering amplitudes in QCD at NNLO to higher orders in the dimensional regulator
• An $n$-point QCD two-loop amplitude
• Symmetric-group decomposition of SU(N) group-theory constraints on four-, five-, and six-point color-ordered amplitudes
• Group-theoretic relations for amplitudes in gauge theories with orthogonal and symplectic groups
• Group-theoretic relations for partial amplitudes in gauge theories with orthogonal group
• All-loop-orders relation between Regge limits of $\mathcal{N}=4$ SYM and $\mathcal{N}=8$ supergravity four-point amplitudes
• Group constraint relations for five-point amplitudes in gauge theories with SO(N) and Sp(2N) groups
• 1-loop Color structures and sunny diagrams