Triple Product Amplitude from Chiral String

In this paper, we proposed a worldsheet construction of a subset of triple product amplitudes proposed by Huang and Remmen. We start with closed bosonic strings but left and right-moving momenta are not necessarily equal. Instead, they satisfy certain conditions. We called them section conditions. These conditions are generalizations of the section condition in double field theory. The vertex operators of chiral strings have nontrivial monodromy, so we interpret them as attached to the end of defects. In the calculation of the amplitude, we not only have to integrate over the moduli space, we also have to sum over different defect configurations. Unitarity and other consistency conditions for chiral string amplitudes are checked. We found the graviton amplitude, the Virasoro amplitude, and also a special kind of amplitude that has one infinite spin tower. Similar kinds of amplitude have appeared in bootstrap literature. The more general $N$-point amplitude could be obtained from a modified KLT relation. The five-point chiral string amplitude is also explicitly calculated.