Singular Solutions in Soft Limits
Abstract
A generalization of the scattering equations on $X(2,n)$, the configuration space of $n$ points on $\mathbb{CP}^1$, to higher dimensional projective spaces was recently introduced by Early, Guevara, Mizera, and one of the authors. One of the new features in $X(k,n)$ with $k>2$ is the presence of both regular and singular solutions in a soft limit. In this work we study soft limits in $X(3,7)$, $X(4,7)$, $X(3,8)$ and $X(5,8)$, find all singular solutions, and show their geometrical configurations. More explicitly, for $X(3,7)$ and $X(4,7)$ we find $180$ and $120$ singular solutions which when added to the known number of regular solutions both give rise to $1\, 272$ solutions as it is expected since $X(3,7)\sim X(4,7)$. Likewise, for $X(3,8)$ and $X(5,8)$ we find $59\, 640$ and $58\, 800$ singular solutions which when added to the regular solutions both give rise to $188\, 112$ solutions. We also propose a classification of all configurations that can support singular solutions for general $X(k,n)$ and comment on their contribution to soft expansions of generalized biadjoint amplitudes.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.02594
 Bibcode:
 2019arXiv191102594C
 Keywords:

 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 27 + 7 pages, 14 figures