139 research outputs found
Free compact boson on branched coverings of the torus
We have studied the free compact boson on a -sheeted covering of the torus
gluing alone branch cuts. It is interesting because when the branched cuts
are chosen to be real, the partition function is related to the -th R\'enyi
entanglement entropy of disjoint intervals in a finite system at finite
temperature. After proposing a canonical homology basis and its dual basis of
the covering surface, we find that the partition function can be written in
terms of theta functions
No-go for tree-level R-symmetry breaking
We show that in gauge mediation models with tree-level R-symmetry breaking
where supersymmetry and R-symmetries are broken by different fields, the
gaugino mass either vanishes at one loop or finds a contribution from
loop-level R-symmetry breaking. Thus tree-level R-symmetry breaking for
phenomenology is either no-go or redundant in the simplest type of models.
Including explicit messenger mass terms in the superpotential with a particular
R-charge arrangement is helpful to bypass the no-go theorem, and the resulting
gaugino mass is suppressed by the messenger mass scale.Comment: 8 pages, 7 figures; v2: discussion on Driac gauginos and references
added; v3: a section on bypassing the no-go added, R-charge notation changed;
v4: typos, EPJC pre-published versio
Two intervals Rényi entanglement entropy of compact free boson on torus
We compute the R\'enyi entanglement entropy of two intervals at equal
time in a circle, for the theory of a 2d compact complex free scalar at finite
temperature. This is carried out by performing functional integral on a genus 3
ramified cover of the torus, wherein the quantum part of the integral is
captured by the four point function of twist fields on the worldsheet torus,
and the classical piece is given by summing over winding modes of the genus 3
surface onto the target space torus. The final result is given in terms of a
product of theta function and certain multi-dimensional theta function. We
demonstrate the T-duality invariance of the result. We also study its low
temperature limit. In the case in which the size of the intervals and of their
separation are much smaller than the whole system, our result is in exact
agreement with the known result for two intervals on an infinite system at zero
temperature \cite{eeoftwo}. In the case in which the separation between the two
intervals is much smaller than the interval length, the leading thermal
corrections take the same universal form as proposed in
\cite{Cardy:2014jwa,Chen:2015cna} for R\'enyi entanglement entropy of a single
interval.Comment: 29 pages, 7 figure
Crossing Lilium Orientals of different ploidy creates Fusarium-resistant hybrid
Oriental hybrid lily is of great commercial value, but it is susceptible to Fusarium disease that causes a significant loss to the production. A diploid Oriental hybrid resistant to Fusarium, Cai-74, was diploidized from triploid obtained from the offspring of tetraploid (from ‘Star Fighter’) and diploid (‘Con Amore’, ‘Acapulco’) by screening the hybrids of different cross combinations following inoculating Fusarium oxysporum to the tissue cultured plantlets in a greenhouse. By analyzing saponins content in bulbs of a number of lily genotypes with a known Fusarium resistance, it was found that the mutant Cai-74 had a much higher content of saponin than its parents. Highly resistant wild _L. dauricum_ had the highest level (4.59mg/g), followed by the resistant Cai-74 with 4.01mg/g. The resistant OT cultivars ‘Conca d’or’ and ‘Robina’ had a higher saponins content (3.70 mg/g) and 2.83 mg/g, than the susceptible Oriental lily cultivars ‘Sorbonne’, ‘Siberia’ and ‘Tiber’. The hybrid Cai-74 had a different karyotype compared with the normal Lilium Oriental hybrid cultivars. The results suggested that Cai-74 carries a chromosomal variation correlated to Fusarium resistance. Cai-74 might be used as a genetic resource for breeding of Fusarium resistant cultivars of Oriental hybrid lilies
On Frobenius Formulas of Power Sequences
Let be relative prime positive integers with
. The Frobenius number is the greatest integer that can not
be written as a nonnegative integer linear combination of the 's. Recently
we developed a combinatorial approach to for . The problem is reduced to solving an easier optimization problem
. In this paper, we use this approach to solve the open problem of
characterizing for the square sequence . Our
point is that the Frobenius number of infinite square
sequence is easier to solve, since the corresponding has a solution in
Number Theory in terms of Lagrange's Four-Square Theorem and related results.
This leads to a solution to the open problem by using Lagrange's Four-Square
Theorem and generating functions. Moreover, the technique can be used for power
sequence, i.e., the case where is a fixed positive integer.Comment: 24 pages 2 tables (Reorganize the contents
Simple Generating Functions for Certain Young Tableaux with Periodic Walls
Recently, Banderier et. al. considered Young tableaux with walls, which are
similar to standard Young tableaux, except that local decreases are allowed at
some walls. We count the numbers of Young tableaux of shape
with walls, that allow local decreases at the -th columns
for all and . We find that they have nice
generating functions (thanks to the OEIS) as follows.
where
is the well-known Catalan generating function.
We prove generalizations of this result. Firstly, we use the Yamanouchi word to
transform Young tableaux with horizontal walls into lattice paths. This results
in a determinant formula. Then by lattice path counting theory, we obtain the
generating functions for the number of lattice paths from to
that never go above the path
, where stand for north and east steps,
respectively. We also obtain exponential formulas for and .
The formula for is thus proved since it is just
specializes at
A Generalization of Mersenne and Thabit Numerical Semigroups
Let be relative prime positive integers with
. The Frobenius number is the largest integer not belonging
to the numerical semigroup generated by . The genus
is the number of positive integer elements that are not in . The Frobenius problem is to find and for a given
sequence . In this paper, we study the Frobenius problem of
and obtain formulas for and
when . Our formulas simplifies further for some special
cases, such as Mersenne and Thabit numerical semigroups. We obtain explicit
formulas for generalized Mersenne and Thabit numerical semigroups and some more
general numerical semigroups
The Frobenius Formula for
Given relative prime positive integers , the
Frobenius number is the largest integer not representable as a linear
combination of the 's with nonnegative integer coefficients. We find the
``Stable" property introduced for the square sequence naturally extends for . This gives a
parallel characterization of as a ``congruence class function" modulo
when is large enough. For orderly sequence , we
find good bound for . In particular we calculate for
, and
- …