On integrands and loop momentum in string and field theory

Abstract

The notion of a unique integrand does not a priori makes sense in field theory: different Feynman diagrams have different loop momenta and there should be no reason to compare them. In string theory, however, a global integrand is natural and allows, for instance, to make explicit the separation between left and right-moving degrees of freedom. However, the significance of this integrand had not really been investigated so far. It is even more important in view of the recently discovered loop monodromies that are related to the duality between color and kinematics in gauge and gravity loop amplitudes. This paper intends to start filling this gap, by presenting a careful definition of the loop momentum in string theory, and describing precisely the resulting global integrand obtained in the field theory limit. We will then apply this technology to write down some monodromy relations at two and three loops, and make contact with the color/kinematics duality.

27 pages, 8 figures. v2: few refs added

References in corpus (24)

• New Relations for Gauge-Theory Amplitudes
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Minimal Basis for Gauge Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Feynman Integrals and Intersection Theory
• Scattering Amplitudes from Intersection Theory
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• Higher genus modular graph functions, string invariants, and their exact asymptotics
• Modular properties of two-loop maximal supergravity and connections with string theory
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• Double-Copy Structure of One-Loop Open-String Amplitudes
• Worldline Green Functions for Arbitrary Feynman Diagrams
• Towards the n-point one-loop superstring amplitude III: One-loop correlators and their double-copy structure
• Monodromy relations from twisted homology
• Towards the n-point one-loop superstring amplitude II: Worldsheet functions and their duality to kinematics
• Towards the n-point one-loop superstring amplitude I: Pure spinors and superfield kinematics
• One-loop monodromy relations on single cuts
• The complex null string, Galilean conformal algebra and scattering equations
• Chiral Closed strings: Four massless states scattering amplitude
• Highly Excited Strings I: Generating Function

Cited by in corpus (15)

• Tree-level amplitudes from the pure spinor superstring
• One-loop Correlators and BCJ Numerators from Forward Limits
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Integrands of loop amplitudes within loop-tree duality
• Superstring loop amplitudes from the field theory limit
• Loop amplitudes monodromy relations and color-kinematics duality
• Positive geometry, local triangulations, and the dual of the Amplituhedron
• Building Bases of Loop Integrands
• Perfecting one-loop BCJ numerators in SYM and supergravity
• Gravity loop integrands from the ultraviolet
• Basis decompositions of genus-one string integrals
• Advanced tools for basis decompositions of genus-one string integrals
• Two-loop superstring five-point amplitudes I: Construction via chiral splitting and pure spinors
• Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands