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Moduli space of paired punctures, cyclohedra and particle pairs on a circle

  • Zhenjie Li
  • Chi ZhangEmail author
Open Access
Regular Article - Theoretical Physics
  • 44 Downloads

Abstract

In this paper, we study a new moduli space \( {\mathrm{\mathcal{M}}}_{n+1}^{\mathrm{c}} \), which is obtained from \( {\mathrm{\mathcal{M}}}_{0,2n+2} \) by identifying pairs of punctures. We find that this space is tiled by 2n − 1n! cyclohedra, and construct the canonical form for each chamber. We also find the corresponding Koba-Nielsen factor can be viewed as the potential of the system of n+1 pairs of particles on a circle, which is similar to the original case of \( {\mathrm{\mathcal{M}}}_{0,n} \) where the system is n−3 particles on a line. We investigate the intersection numbers of chambers equipped with Koba-Nielsen factors. Then we construct cyclohedra in kinematic space and show that the scattering equations serve as a map between the interior of worldsheet cyclohedron and kinematic cyclohedron. Finally, we briefly discuss string-like integrals over such moduli space.

Keywords

Scattering Amplitudes Differential and Algebraic Geometry Bosonic Strings 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.CAS Key Laboratory of Theoretical Physics, Institute of Theoretical PhysicsChinese Academy of SciencesBeijingChina
  2. 2.School of Physical SciencesUniversity of Chinese Academy of SciencesBeijingChina

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