One-loop monodromy relations on single cuts

Abstract

The discovery of colour-kinematic duality has led to significant progress in the computation of scattering amplitudes in quantum field theories. At tree level, the origin of the duality can be traced back to the monodromies of open-string amplitudes. This construction has recently been extended to all loop orders. In the present paper, we dissect some consequences of these new monodromy relations at one loop. We use single cuts in order to relate them to the tree-level relations. We show that there are new classes of kinematically independent single-cut amplitudes. Then we turn to the Feynman diagrammatics of the string-theory monodromy relations. We revisit the string-theoretic derivation and argue that some terms, that vanish upon integration in string and field theory, provide a characterisation of momentum-shifting ambiguities in these representations. We observe that colour-dual representations are compatible with this analysis.

24 pages + appendices + refs; v3 minor corrections, journal version

References in corpus (24)

• New Relations for Gauge-Theory Amplitudes
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Minimal Basis for Gauge Theory Amplitudes
• Direct extraction of one-loop integral coefficients
• The Momentum Kernel of Gauge and Gravity Theories
• The Kinematic Algebra From the Self-Dual Sector
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• From loops to trees by-passing Feynman's theorem
• Gravity and Yang-Mills Amplitude Relations
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• A Tree-Loop Duality Relation at Two Loops and Beyond
• Loops and trees
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• On the singular behaviour of scattering amplitudes in quantum field theory
• Unitarity of Superstring Field Theory
• One-Loop Gluonic Amplitudes from Single Unitarity Cuts
• Single Cut Integration
• BCJ relations from a new symmetry of gauge-theory amplitudes