Fractional chaotic inflation in the lights of PLANCK and BICEP2

In the lights of current BICEP2 observations accompanied with the PLANCK satellite results, it has been observed that the simple single field chaotic inflationary models provide a good agreement with their spectral index n_s and large tensor-to-scalar ratio r (0.15 <r <0.26). To explore the other simple models, we consider the fractional-chaotic inflationary potentials of the form V_0 phi^(a/b) where a and b are relatively prime. We show that such kind of inflaton potentials can be realized elegantly in the supergravity framework with generalized shift symmetry and a nature bound a/b < 4 for consistency. Especially, for the number of e-folding from 50 to 60 and some a/b from 2 to 3, our predictions are nicely within at least 1 $\sigma$ region in the r-n_s plane. We also present a systematic investigation of such chaotic inflationary models with fractional exponents to explore the possibilities for the enhancement in the magnitude of running of spectral index (\alpha_{n_s}) beyond the simplistic models.Comment: 16 pages, 5 figures, references added, published in PL

SU(5) Symmetry of spdfg Interacting Boson Model

The extended interacting boson model with s-, p-, d-, f- and g-bosons being included (spdfg IBM) are investigated. The algebraic structure including the generators, the Casimir operators of the groups at the SU(5) dynamical symmetry and the branching rules of the irreducible representation reductions along the group chain are obtained. The typical energy spectrum of the Symmetry is given.Comment: 12 pages, 2 figure

The GRB-Supernova Connection

Long-duration gamma-ray bursts (GRBs) are believed to be produced by the core collapse of massive stars and hence to be connected with supernovae (SNe). Indeed, for four pairs of GRBs and SNe, spectroscopically confirmed connection has been firmly established. For more than a dozen of GRBs the SN signature (the `red bump') has been detected in the afterglow lightcurves. Based on the four pairs of GRBs and SNe with spectroscopically confirmed connection a tight correlation was found between the peak spectral energy of GRBs and the peak bolometric luminosity of the underlying SNe. The recent discovery of X-ray flash 080109 associated with a normal core-collapse SN 2008D confirmed this relation and extended the GRB-SN connection. Progress on the GRB-SN connection is briefly reviewed.Comment: 6 pages, 5 figures. To appear in the proceedings of "2008 Nanjing GRB conference", Nanjing, 23-27 June 200

ICE-closed subcategories and epibricks over one-point extensions

Let $B$ be the one-point extension algebra of $A$ by an $A$-module $M$. We proved that every ICE-closed subcategory in$\mod A$ can be extended to be some ICE-closed subcategories in$\mod B$.In the same way, every epibrick in $\mod A$ can be extended to be some epibricks in $\mod B$.The number of ICE-closed subcategories in $\mod B$ and the number of ICE-closed subcategories in $\mod A$ are denoted respectively as $m$, $n$.We can conclude the following inequality:$$m \geq 2n$$ This is the analogical in epibricks.As an application, we can get some wide $\tau$-tilting modules of $B$ by wide $\tau$-tilting modules of $A$.Comment: 10 page

Phase transitions in a holographic s+p model with backreaction

In a previous paper (arXiv:1309.2204, JHEP 1311 (2013) 087), we present a holographic s+p superconductor model with a scalar triplet charged under an SU(2) gauge field in the bulk. We also study the competition and coexistence of the s-wave and p-wave orders in the probe limit. In this work we continue to study the model by considering the full back-reaction The model shows a rich phase structure and various condensate behaviors such as the "n-type" and "u-type" ones, which are also known as reentrant phase transitions in condensed matter physics. The phase transitions to the p-wave phase or s+p coexisting phase become first order in strong back-reaction cases. In these first order phase transitions, the free energy curve always forms a swallow tail shape, in which the unstable s+p solution can also play an important role. The phase diagrams of this model are given in terms of the dimension of the scalar order and the temperature in the cases of eight different values of the back reaction parameter, which show that the region for the s+p coexisting phase is enlarged with a small or medium back reaction parameter, but is reduced in the strong back-reaction cases.Comment: 15 pages(two-column), 9 figure