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.
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Li, Z., Zhang, C. Moduli space of paired punctures, cyclohedra and particle pairs on a circle. J. High Energ. Phys. 2019, 29 (2019). https://doi.org/10.1007/JHEP05(2019)029
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DOI: https://doi.org/10.1007/JHEP05(2019)029