Lorentzian contours for tree-level string amplitudes

Abstract

We engineer compact contours on the moduli spaces of genus-zero Riemann surfaces that achieve analytic continuation from Euclidean to Lorentzian worldsheets. These generalized Pochhammer contours are based on the combinatorics of associahedra and make the analytic properties of tree-level amplitudes entirely manifest for any number and type of external strings. We use them in practice to perform first numerical computations of open and closed string amplitudes directly in the physical kinematics for $n=4,5,6,7,8,9$. We provide a code that allows anyone to do such computations.

arXiv comment27 pages, ancillary Mathematica notebook for numerical string amplitude computations

References in corpus (23)

• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• The Momentum Kernel of Gauge and Gravity Theories
• Open & Closed vs. Pure Open String Disk Amplitudes
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Aspects of Scattering Amplitudes and Moduli Space Localization
• Moduli of J-Holomorphic Curves with Lagrangian Boundary Conditions and Open Gromov-Witten Invariants for an $S^1$-Equivariant Pair
• The Polynomial Form of the Scattering Equations
• Inverse of the String Theory KLT Kernel
• Tree-level amplitudes from the pure spinor superstring
• Tropical Feynman integration in the Minkowski regime
• String Field Theory as World-sheet UV Regulator
• Intersection numbers of twisted cycles and the correlation functions of the conformal field theory II
• Disk Scattering of Open and Closed Strings (I)
• Graviton as a Pair of Collinear Gauge Bosons
• Multiple zeta values and periods of moduli spaces ${\mathfrak{M}}_{0,n}$
• Unitarity Cuts of the Worldsheet
• Coaction and double-copy properties of configuration-space integrals at genus zero
• Evaluating one-loop string amplitudes
• A Contour Integral Representation for the Dual Five-Point Function and a Symmetry of the Genus Four Surface in R6
• Four Lectures on Euler Integrals
• Deformations of bordered Riemann surfaces and associahedral polytopes
• Regge Limit of One-Loop String Amplitudes
• A Subtraction Scheme for Feynman Integrals

Cited by in corpus (3)

• Open String Amplitudes: Singularities, Asymptotics, and New Representations
• Lectures in Quantum Gravity
• One-loop four-graviton string amplitude at finite ${\alpha }^{\prime }$