26,841 research outputs found
Moduli Space of Paired Punctures, Cyclohedra and Particle Pairs on a Circle
In this paper, we study a new moduli space ,
which is obtained from by identifying pairs of
punctures. We find that this space is tiled by 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
pairs of particles on a circle, which is similar to the original case of
where the system is 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.Comment: 23 pages, 7 figure
One loop amplitude from null string
We generalize the CHY formalism to one-loop level, based on the framework of
the null string theory. The null string, a tensionless string theory, produces
the same results as the ones from the chiral ambitwistor string theory, with
the latter believed to give a string interpretation of the CHY formalism. A key
feature of our formalism is the interpretation of the modular parameters. We
find that the modular transformation invariance of the ordinary string
theory does not survive in the case of the null string theory. Treating the
integration over the modular parameters this way enable us to derive the n-gons
scattering amplitude in field theory, thus proving the n-gons conjecture.Comment: 18 pages, 2 figure
A Generalization of the Doubling Construction for Sums of Squares Identities
The doubling construction is a fast and important way to generate new
solutions to the Hurwitz problem on sums of squares identities from any known
ones. In this short note, we generalize the doubling construction and obtain
from any given admissible triple a series of new ones
for all positive integer , where is the
Hurwitz-Radon function
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