Closed strings as single-valued open strings: A genus-zero derivation

Abstract

Based on general mathematical assumptions we give an independent, elementary derivation of a theorem by Francis Brown and Clément Dupont which states that tree-level amplitudes of closed and open strings are related through the single-valued map `sv'. This relation can be traced back to the underlying moduli-space integrals over punctured Riemann surfaces of genus zero. The sphere integrals $J$ in closed-string amplitudes and the disk integrals $Z$ in open-string amplitudes are shown to obey $J=\mathrm{sv}Z$.

19 pages

References in corpus (12)

• Minimal Basis for Gauge Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• Scattering Amplitudes from Intersection Theory
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Non-abelian $Z$-theory: Berends-Giele recursion for the ${\alpha }^{\prime }$-expansion of disk integrals
• Multi-Gluon Scattering in Open Superstring Theory
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Matching the $D^6{\mathcal{R}}^4$ interaction at two-loops
• Heterotic and bosonic string amplitudes via field theory
• Amplitude relations in heterotic string theory and Einstein-Yang-Mills
• Higher genus modular graph functions, string invariants, and their exact asymptotics
• SV-map between Type I and Heterotic Sigma Models

Cited by in corpus (19)

• Single-valued integration and superstring amplitudes in genus zero
• The AdS Virasoro-Shapiro Amplitude
• AdS Virasoro-Shapiro from single-valued periods
• Tree-level amplitudes from the pure spinor superstring
• String amplitudes from field-theory amplitudes and vice versa
• All-order differential equations for one-loop closed-string integrals and modular graph forms
• One-loop open-string integrals from differential equations: all-order alpha'-expansions at n points
• Generating series of all modular graph forms from iterated Eisenstein integrals
• String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
• Lauricella hypergeometric functions, unipotent fundamental groups of the punctured Riemann sphere, and their motivic coactions
• Properties of infinite product amplitudes: Veneziano, Virasoro, and Coon
• Multiple zeta values in deformation quantization
• Coaction and double-copy properties of configuration-space integrals at genus zero
• Modular graph forms from equivariant iterated Eisenstein integrals
• The Kaluza-Klein AdS Virasoro-Shapiro Amplitude near Flat Space
• Integrating three-loop modular graph functions and transcendentality of string amplitudes
• Type II superstring amplitude at one-loop and transcendentality
• CHY Theory for Several Fields
• Twisted de Rham theory for string double copy in AdS