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Related Experiment Video

Updated: Nov 11, 2025

Setting Limits on Supersymmetry Using Simplified Models
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Single-Valued Integration and Superstring Amplitudes in Genus Zero.

Francis Brown1, Clément Dupont2

  • 1All Souls College, Oxford, Oxford, OX1 4AL UK.

Communications in Mathematical Physics
|March 24, 2021
PubMed
Summary

This study reveals that closed string amplitudes are single-valued projections of open string amplitudes. This finding, using single-valued integration, confirms a key conjecture in string theory and unifies open and closed string theories.

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Area of Science:

  • String Theory
  • Quantum Field Theory
  • Mathematical Physics

Background:

  • Perturbation theory in string theory involves complex calculations.
  • Existing methods lack a unified approach for open and closed string amplitudes.
  • The double copy framework suggests deep connections between different string theories.

Purpose of the Study:

  • To develop a unified framework for calculating tree-level open and closed string amplitudes.
  • To prove Stieberger's conjecture relating closed and open string amplitudes.
  • To establish a connection between motivic structures and string amplitudes.

Main Methods:

  • Application of single-valued integration techniques.
  • Utilizing dihedral coordinates on moduli spaces of genus zero curves.
  • Development of a canonical regularization for string perturbation amplitudes.

Main Results:

  • Open and closed string amplitudes admit Laurent expansions with multiple zeta values.
  • A motivic Laurent expansion is proven to exist, linking open and closed string amplitudes.
  • The KLT formula is derived from a single-valued formalism.

Conclusions:

  • Confirms Stieberger's conjecture: closed string amplitudes are single-valued projections of open string amplitudes.
  • Demonstrates the power of single-valued integration in unifying string theory calculations.
  • Provides a new perspective on the double copy structure in quantum gravity.