389 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
Crystal structure and electronic structure of quaternary semiconductors CuZnTiSe and CuZnTiS for solar cell absorber
We design two new I2-II-IV-VI4 quaternary semiconductors CuZnTiSe and
CuZnTiS, and systematically study the crystal and electronic structure
by employing first-principles electronic structure calculations. Among the
considered crystal structures, it is confirmed that the band gaps of
CuZnTiSe and CuZnTiS originate from the full occupied Cu 3
valence band and unoccupied Ti 3 conducting band, and kesterite structure
should be the ground state. Furthermore, our calculations indicate that
CuZnTiSe and CuZnTiS have comparable band gaps with
CuZnTSe and CuZnTS, but almost twice larger absorption
coefficient . Thus, the materials are expected to be candidate
materials for solar cell absorber.Comment: 4 pages, 4 figure
A nice two-loop next-to-next-to-MHV amplitude in super-Yang-Mills
We study a scalar component of the 8-point
next-to-next-to-maximally-helicity-violating (NMHV) amplitude at two-loop
level in super-Yang-Mills theory; it has a leading singularity
proportional to the inverse of the four-mass-box square root and receives
contributions from only two types of non-trivial integrals with one-loop
infrared (IR) divergences. We compute such two-loop 8-point integrals by taking
(double-)collinear limits of certain finite, dual-conformal-invariant
integrals, and they nicely give the IR-safe ratio function after subtracting
divergences. As the first genuine two-loop NMHV amplitude computed
explicitly, we find remarkable structures in its symbol and alphabet: similar
to the next-to-MHV (NMHV) case, there are still 9 algebraic letters associated
with the square root, and the latter also becomes a letter for the first time;
unlike the NMHV case, such algebraic letters appear at either one or all of the
second, third and last entry, and the part with three odd letters is
particularly simple.Comment: 20 pages, 2 figures and an ancillary file containing symbols of
two-loop integrals and the ratio functio
Notes on cluster algebras and some all-loop Feynman integrals
We study cluster algebras for some all-loop Feynman integrals, including
box-ladder, penta-box-ladder, and (seven-point) double-penta-ladder integrals.
In addition to the well-known box ladder whose symbol alphabet is , we show that penta-box ladder has an alphabet of and
provide strong evidence that the alphabet of double-penta ladder can be
identified with a cluster algebra. We relate the symbol letters to the
variables of cluster configuration space, which provide a
gauge-invariant description of the cluster algebra, and we find various
sub-algebras associated with limits of the integrals. We comment on constraints
similar to extended-Steinmann relations or cluster adjacency conditions on
cluster function spaces. Our study of the symbol and alphabet is based on the
recently proposed Wilson-loop representation, which allows us to
predict higher-loop alphabet recursively; by applying such recursions to
six-dimensional hexagon integrals, we also find and cluster
functions for the two-mass-easy and three-mass-easy case, respectively.Comment: 28 pages, several figures; v2: typos corrected, functions of ladder
integrals computed to higher loops; v3: more examples of double-penta-ladder
integrals and discussions about their alphabet adde
The symbol and alphabet of two-loop NMHV amplitudes from equations
We study the symbol and the alphabet for two-loop NMHV amplitudes in planar
super-Yang-Mills from the equations, which provide a
first-principle method for computing multi-loop amplitudes. Starting from
one-loop NMHV ratio functions, we explain in detail how to use
equations to obtain the total differential of two-loop -point NMHV
amplitudes, whose symbol contains letters that are algebraic functions of
kinematics for . We present explicit formula with nice patterns for
the part of the symbol involving algebraic letters for all multiplicities, and
we find multiplicative-independent letters for a given square root of
Gram determinant, with depending on the number of particles
involved in the square root. We also observe that these algebraic letters can
be found as poles of one-loop four-mass leading singularities with MHV or NMHV
trees. As a byproduct of our algebraic results, we find a large class of
components of two-loop NMHV, which can be written as differences of two
double-pentagon integrals, particularly simple and absent of square roots. As
an example, we present the complete symbol for whose alphabet contains
rational letters, in addition to the independent
algebraic ones. We also give all-loop NMHV last-entry conditions for all
multiplicities.Comment: 33 pages, 1 figure, revised version, typo corrected, accepted in JHE
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