Unitarity Cuts of the Worldsheet

Abstract

We compute the imaginary parts of genus-one string scattering amplitudes. Following Witten's $i\epsilon$ prescription for the integration contour on the moduli space of worldsheets, we give a general algorithm for computing unitarity cuts of the annulus, Möbius strip, and torus topologies exactly in ${\alpha }^{\prime }$. With the help of tropical analysis, we show how the intricate pattern of thresholds (normal and anomalous) opening up arises from the worldsheet computation. The result is a manifestly-convergent representation of the imaginary parts of amplitudes, which has the analytic form expected from Cutkosky rules in field theory, but bypasses the need for performing laborious sums over the intermediate states. We use this representation to study various physical aspects of string amplitudes, including their behavior in the $(s,t)$ plane, exponential suppression, decay widths of massive strings, total cross section, and low-energy expansions. We find that planar annulus amplitudes exhibit a version of low-spin dominance: at any finite energy, only a finite number of low partial-wave spins give an appreciable contribution to the imaginary part.

arXiv comment87 pages

References in corpus (46)

• High Energy Colliders as Black Hole Factories: The End of Short Distance Physics
• The EFT-Hedron
• A Model for High Energy Scattering in Quantum Gravity
• Two-Loop Superstrings VI: Non-Renormalization Theorems and the 4-Point Function
• Motivic Multiple Zeta Values and Superstring Amplitudes
• Explicit solutions of the multi-loop integral recurrence relations and its application
• The low energy expansion of the one-loop type II superstring amplitude
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• Low energy expansion of the four-particle genus-one amplitude in type II superstring theory
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• On the modular structure of the genus-one Type II superstring low energy expansion
• The closed-string 3-loop amplitude and S-duality
• Aspects of Scattering Amplitudes and Moduli Space Localization
• Cutkosky Rules for Superstring Field Theory
• Super-Poincare Covariant Two-Loop Superstring Amplitudes
• String Balls at the LHC and Beyond
• Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
• The Box Graph In Superstring Theory
• Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds
• Tropical Amplitudes
• Tropical Monte Carlo quadrature for Feynman integrals
• Crossing Symmetry in the Planar Limit
• Momentum Analyticity and Finiteness of the 1-Loop Superstring Amplitude
• Unitarity of Superstring Field Theory
• On Unitarity of Tree-Level String Amplitudes
• Feynman Polytopes and the Tropical Geometry of UV and IR Divergences
• String Field Theory as World-sheet UV Regulator
• Exploring transcendentality in superstring amplitudes
• Evaluation of the CHY Gauge Amplitude
• Decay of long-lived massive closed superstring states: Exact results
• One-loop Correlators and BCJ Numerators from Forward Limits
• What is the $i\epsilon$ for the S-matrix?
• The covariant perturbative string spectrum
• Superstring loop amplitudes from the field theory limit
• Monodromy relations from twisted homology
• Two-loop superstring five-point amplitudes II: Low energy expansion and S-duality
• Unitarity of the Box Diagram
• Dispersion Relations in String Theory
• Loop amplitudes monodromy relations and color-kinematics duality
• Hepp's bound for Feynman graphs and matroids
• Snowmass White Paper: String Perturbation Theory
• Periods and Superstring Amplitudes
• String theory integrands and supergravity divergences
• Open-string integrals with multiple unintegrated punctures at genus one
• Modular Graph Forms and Scattering Amplitudes in String Theory
• The SAGEX Review on Scattering Amplitudes, Chapter 2: An Invitation to Color-Kinematics Duality and the Double Copy

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