7,685 research outputs found
Computation of Contour Integrals on
Contour integrals of rational functions over , the moduli
space of -punctured spheres, have recently appeared at the core of the
tree-level S-matrix of massless particles in arbitrary dimensions. The contour
is determined by the critical points of a certain Morse function on . The integrand is a general rational function of the puncture
locations with poles of arbitrary order as two punctures coincide. In this note
we provide an algorithm for the analytic computation of any such integral. The
algorithm uses three ingredients: an operation we call general KLT, Petersen's
theorem applied to the existence of a 2-factor in any 4-regular graph and
Hamiltonian decompositions of certain 4-regular graphs. The procedure is
iterative and reduces the computation of a general integral to that of simple
building blocks. These are integrals which compute double-color-ordered partial
amplitudes in a bi-adjoint cubic scalar theory.Comment: 36+11 p
Bose-Hubbard model on two-dimensional line graphs
We construct a basis for the many-particle ground states of the positive
hopping Bose-Hubbard model on line graphs of finite 2-connected planar
bipartite graphs at sufficiently low filling factors. The particles in these
states are localized on non-intersecting vertex-disjoint cycles of the line
graph which correspond to non-intersecting edge-disjoint cycles of the original
graph. The construction works up to a critical filling factor at which the
cycles are close-packed.Comment: 9 pages, 5 figures, figures and conclusions update
Hamiltonian Cycles on a Random Three-coordinate Lattice
Consider a random three-coordinate lattice of spherical topology having 2v
vertices and being densely covered by a single closed, self-avoiding walk, i.e.
being equipped with a Hamiltonian cycle. We determine the number of such
objects as a function of v. Furthermore we express the partition function of
the corresponding statistical model as an elliptic integral.Comment: 10 pages, LaTeX, 3 eps-figures, one reference adde
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