Monodromy Relations in Higher-Loop String Amplitudes

Abstract

New monodromy relations of loop amplitudes are derived in open string theory. We particularly study N-point one-loop amplitudes described by a world-sheet cylinder (planar and non-planar) and derive a set of relations between subamplitudes of different color orderings. Various consistency checks are performed by matching alpha'-expansions of planar and non-planar amplitudes involving elliptic iterated integrals with the resulting periods giving rise to two sets of multiple elliptic zeta values. The latter refer to the two homology cycles on the once-punctured complex elliptic curve and the monodromy equations provide relations between these two sets of multiple elliptic zeta values. Furthermore, our monodromy relations involve new objects for which we present a tentative interpretation in terms of open string scattering amplitudes in the presence of a non-trivial gauge field flux. Finally, we provide an outlook on how to generalize the new monodromy relations to the non-oriented case and beyond the one-loop level. Comparing a subset of our results with recent findings in the literature we find therein several serious issues related to the structure and significance of monodromy phases and the relevance of missed contributions from contour integrations.

75 pages, LaTeX; v2: Final version to appear in Nucl. Phys. B. Several minor typos removed. Not any changes in results and conclusions

References in corpus (5)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• New Relations for Einstein-Yang-Mills Amplitudes
• Graviton as a Pair of Collinear Gauge Bosons
• Graviton Amplitudes from Collinear Limits of Gauge Amplitudes

Cited by in corpus (43)

• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• The $\epsilon$-form of the differential equations for Feynman integrals in the elliptic case
• Analytic results for the planar double box integral relevant to top-pair production with a closed top loop
• The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter
• The unequal mass sunrise integral expressed through iterated integrals on ${\overline{\mathcal{M}}}_{1,3}$
• New BCJ representations for one-loop amplitudes in gauge theories and gravity
• Heterotic and bosonic string amplitudes via field theory
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Double Copy for Celestial Amplitudes
• Gluons and gravitons at one loop from ambitwistor strings
• On the kinematic algebra for BCJ numerators beyond the MHV sector
• From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop
• Two-Loop Scattering Amplitudes from Ambitwistor Strings: from Genus Two to the Nodal Riemann Sphere
• Numerical evaluation of iterated integrals related to elliptic Feynman integrals
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Plane wave backgrounds and colour-kinematics duality
• Unraveling conformal gravity amplitudes
• Tree-level amplitudes from the pure spinor superstring
• One-loop Correlators and BCJ Numerators from Forward Limits
• One-loop open-string integrals from differential equations: all-order alpha'-expansions at n points
• Twisted elliptic multiple zeta values and non-planar one-loop open-string amplitudes
• Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality
• Monodromy relations from twisted homology
• Superstring loop amplitudes from the field theory limit
• One-loop monodromy relations on single cuts
• Loop amplitudes monodromy relations and color-kinematics duality
• On integrands and loop momentum in string and field theory
• Modular transformations of elliptic Feynman integrals
• One-loop Amplitudes for N=2 Homogeneous Supergravities
• Coaction and double-copy properties of configuration-space integrals at genus zero
• Poincaré series for modular graph forms at depth two. I. Seeds and Laplace systems
• A double copy from twisted (co)homology at genus one
• Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD
• BCJ, worldsheet quantum algebra and KZ equations
• Basis decompositions of genus-one string integrals
• On new theta identities of fermion correlation functions on genus g Riemann surfaces
• Einstein Yang-Mills Amplitudes from Intersections of Twisted Forms
• Next-to-MHV Yang-Mills kinematic algebra
• Open-string integrals with multiple unintegrated punctures at genus one
• Advanced tools for basis decompositions of genus-one string integrals
• Open & Closed vs. Pure Open String One-Loop Amplitudes
• Twisted de Rham theory for string double copy in AdS
• One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands