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arXiv · 1812.10727

Moduli Space of Paired Punctures, Cyclohedra and Particle Pairs on a Circle

Zhenjie Li·Chi Zhang
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Abstract

In this paper, we study a new moduli space $\mathcal{M}_{n+1}^{\mathrm{c}}$, which is obtained from $\mathcal{M}_{0,2n+2}$ by identifying pairs of punctures. We find that this space is tiled by $2^{n-1}n!$ 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 $\mathcal{M}_{0,n}$ 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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Zhenjie Li, Chi Zhang. 2018-12-27. Moduli Space of Paired Punctures, Cyclohedra and Particle Pairs on a Circle. https://doi.org/10.1007/jhep05(2019)029

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