4,438 research outputs found
KLT-type relations for QCD and bicolor amplitudes from color-factor symmetry
Color-factor symmetry is used to derive a KLT-type relation for tree-level
QCD amplitudes containing gluons and an arbitrary number of massive or massless
quark-antiquark pairs, generalizing the expression for Yang-Mills amplitudes
originally postulated by Bern, De Freitas, and Wong. An explicit expression is
given for all amplitudes with two or fewer quark-antiquark pairs in terms of
the (modified) momentum kernel.
We also introduce the bicolor scalar theory, the "zeroth copy" of QCD,
containing massless biadjoint scalars and massive bifundamental scalars,
generalizing the biadjoint scalar theory of Cachazo, He, and Yuan. We derive
KLT-type relations for tree-level amplitudes of biadjoint and bicolor theories
using the color-factor symmetry possessed by these theories.Comment: 24 pages, 2 figures; v2: added referenc
Dyck path triangulations and extendability
We introduce the Dyck path triangulation of the cartesian product of two
simplices . The maximal simplices of this
triangulation are given by Dyck paths, and its construction naturally
generalizes to produce triangulations of
using rational Dyck paths. Our study of the Dyck path triangulation is
motivated by extendability problems of partial triangulations of products of
two simplices. We show that whenever , any triangulation of
extends to a unique triangulation of
. Moreover, with an explicit construction, we
prove that the bound is optimal. We also exhibit interesting
interpretations of our results in the language of tropical oriented matroids,
which are analogous to classical results in oriented matroid theory.Comment: 15 pages, 14 figures. Comments very welcome
Rational Dyck Paths in the Non Relatively Prime Case
We study the relationship between rational slope Dyck paths and invariant
subsets of extending the work of the first two authors in the
relatively prime case. We also find a bijection between --Dyck paths
and -tuples of -Dyck paths endowed with certain gluing data. These
are the first steps towards understanding the relationship between rational
slope Catalan combinatorics and the geometry of affine Springer fibers and knot
invariants in the non relatively prime case.Comment: 25 pages, 9 figure
- β¦