A tree expansion formula of a homology intersection numbers on the configuration space ${\mathcal{M}}_{0,n}$

Abstract

In \cite{M}, Sebastian Mizera discovered a tree expansion formula of a homology intersection number on the configuration space ${\mathcal{M}}_{0,n}$. The formula originates in a study of Kawai-Lewellen-Tye relation in string theory. In this paper, we give an elementary proof of the formula. The basic ingredients are the combinatorics of the real moduli space ${\overline{\mathcal{M}}}_{0,n}(\mathbb{R})$ and a combinatorial identity related to the face number of the associahedron.

arXiv comment17 pages, 6 figures. Comments are welcome

References in corpus (6)

• Scattering of Massless Particles: Scalars, Gluons and Gravitons
• The Momentum Kernel of Gauge and Gravity Theories
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Factorization of Chiral String Amplitudes
• Inverse of the String Theory KLT Kernel
• Twisted cycles and twisted period relations for Lauricella's hypergeometric function F_C