Abstract
Abstract
In this paper, we study a new moduli space
$$ {\mathrm{\mathcal{M}}}_{n+1}^{\mathrm{c}} $$
ℳ
n
+
1
c
, which is obtained from
$$ {\mathrm{\mathcal{M}}}_{0,2n+2} $$
ℳ
0
,
2
n
+
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
$$ {\mathrm{\mathcal{M}}}_{0,n} $$
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.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
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