Euler's partition theorem for all moduli and new companions to Rogers-Ramanujan-Andrews-Gordon identities

In this paper, we give a conjecture, which generalises Euler's partition theorem involving odd parts and different parts for all moduli. We prove this conjecture for two family partitions. We give $q$-difference equations for the related generating function if the moduli is three. We provide new companions to Rogers-Ramanujan-Andrews-Gordon identities under this conjecture.Comment: 12 pages, revised versio

Moduli Stabilization in Type IIB Flux Compactifications

In the present paper, we reexamine the moduli stabilization problem of the Type IIB orientifolds with one complex structure modulus in a modified two-step procedure. The full superpotential including both the 3-form fluxes and the non-perturbative corrections is used to yield a F-term potential. This potential is simplified by using one optimization condition to integrate the dilaton field out. It is shown that having a locally stable supersymmetric Anti-deSitter vacuum is not inevitable for these orientifolds, which depend strongly upon the details of the flux parameters. For those orientifolds that have stable/metastable supersymmetry-broken minima of the F-term potential, the deSitter vacua might emerge even without the inclusion of the uplifting contributions.Comment: 10 pages, LaTeX2e style. The paper is rewritten in ver3 with more references adde

Andreev Bound states in One Dimensional Topological Superconductor

We study the charge character of the Andreev bound states (ABSs) in one-dimensional topological superconductors with spatial inversion symmetry (SIS) breaking. Despite the absence of the SIS, we show a hidden symmetry for the Bogoliubov de Gennes equations around Fermi points in addition to the particle-hole symmetry. This hidden symmetry protects that the charge of the ABSs is solely dependent on the corresponding Fermi velocities. On the other hand, if the SIS is present, the ABSs are charge neutral, similar to Majorana fermions. We demonstrate that the charge of the ABSs can be experimentally measured in the tunneling transport spectroscopy from the resonant differential tunneling conductance.Comment: 4 pages plus appendix; 4 figure