One-loop matrix elements of effective superstring interactions: ${\alpha }^{\prime }$-expanding loop integrands

Abstract

In the low-energy effective action of string theories, non-abelian gauge interactions and supergravity are augmented by infinite towers of higher-mass-dimension operators. We propose a new method to construct one-loop matrix elements with insertions of operators $D^{2k}{F}^n$ and $D^{2k}{R}^n$ in the tree-level effective action of type-I and type-II superstrings. Inspired by ambitwistor string theories, our method is based on forward limits of moduli-space integrals using string tree-level amplitudes with two extra points, expanded in powers of the inverse string tension ${\alpha }^{\prime }$. Similar to one-loop ambitwistor computations, intermediate steps feature non-standard linearized Feynman propagators which eventually recombine to conventional quadratic propagators. With linearized propagators the loop integrand of the matrix elements obey one-loop versions of the monodromy and KLT relations. We express a variety of four- and five-point examples in terms of quadratic propagators and formulate a criterion on the underlying genus-one correlation functions that should make this recombination possible at all orders in ${\alpha }^{\prime }$. The ultraviolet divergences of the one-loop matrix elements are crosschecked against the non-separating degeneration of genus-one integrals in string amplitudes. Conversely, our results can be used as a constructive method to determine degenerations of elliptic multiple zeta values and modular graph forms at arbitrary weight.

71 pages plus appendices and ancillary files; v2: matching published version; v3: Minor corrections in (4.29), (4.49), (4.50), (7.3) and (C.3)

References in corpus (25)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• The EFT-Hedron
• Form Factors in N=4 Super Yang-Mills and Periodic Wilson Loops
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• Multi-Gluon Scattering in Open Superstring Theory
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• Six Gluon Open Superstring Disk Amplitude, Multiple Hypergeometric Series and Euler-Zagier Sums
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• Two-Loop Renormalization of Quantum Gravity Simplified
• String predictions for near future colliders from one-loop scattering amplitudes around D-brane worlds
• Effective action of type II superstring theories at order ${\alpha }^{\prime 3}$: NS-NS couplings
• Current Algebra on the Torus
• Composing Effective Prediction at Five Points
• One-loop Correlators and BCJ Numerators from Forward Limits
• One-loop monodromy relations on single cuts
• CHY-Graphs on a Torus
• Explaining Pure Spinor Superspace
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• Form factor recursion relations at loop level
• Ambitwistor Integrands from Tensionless Chiral Superstring Integrands
• Chiral Closed strings: Four massless states scattering amplitude
• On Chiral Splitting and the Ambitwistor String
• Modular Graph Forms and Scattering Amplitudes in String Theory