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Home > Journal of High Energy Physics (Springer/SISSA) > Moduli space of paired punctures, cyclohedra and particle pairs on a circle |

Li, Zhenjie (0000000119573309, CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China) (0000 0004 1797 8419, School of Physical Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing, 100049, China) ; Zhang, Chi (0000000119573309, CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China) (0000 0004 1797 8419, School of Physical Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing, 100049, China)

07 May 2019

**Abstract: **In this paper, we study a new moduli space ℳ n + 1 c $$ {\mathrm{\mathcal{M}}}_{n+1}^{\mathrm{c}} $$ , which is obtained from ℳ 0 , 2 n + 2 $$ {\mathrm{\mathcal{M}}}_{0,2n+2} $$ 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 ℳ 0 , n $$ {\mathrm{\mathcal{M}}}_{0,n} $$ 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.

**Published in: ****JHEP 1905 (2019) 029**
**Published by: **Springer/SISSA

**DOI: **10.1007/JHEP05(2019)029

**arXiv: **1812.10727

**License: **CC-BY-4.0