Coverings and Truncations of Graded Selfinjective Algebras

Let $\Lambda$ be a graded self-injective algebra. We describe its smash product \Lambda# k\mathbb Z^* with the group $\mathbb Z$, its Beilinson algebra and their relationship. Starting with $\Lambda$, we construct algebras with finite global dimension, called $\tau$-slice algebras, we show that their trivial extensions are all isomorphic, and their repetitive algebras are the same \Lambda# k\mathbb Z^*. There exist $\tau$-mutations similar to the BGP reflections for the $\tau$-slice algebras. We also recover Iyama's absolute $n$-complete algebra as truncation of the Koszul dual of certain self-injective algebra.Comment: Manuscript revised, introduction and abstract rewritte

On nn-translation algebras

Motivated by Iyama's higher representation theory, we introduce $n$-translation quivers and $n$-translation algebras. The classical $\mathbb Z Q$ construction of the translation quiver is generalized to construct an $(n+1)$-translation quiver from an $n$-translation quiver, using trivial extension and smash product. We prove that the quadratic dual of $n$-translation algebras have $(n-1)$-almost splitting sequences in the category of its projective modules. We also present a non-Koszul $1$-translation algebra whose trivial extension is $2$-translation algebra, thus also provides a class of examples of $(3,m-1)$-Koszul algebras (and also a class of $(m-1,3)$-Koszul algebras) for all $m \ge 2$.Comment: The paper is revised, according to the referees' suggestions and comments. The definitions of $n$-translation quiver, admissibility are rewritten, and the results related to these definition are revised. The results concerning $n$-almost split sequence is revised. The Section 7 is removed and Section 6 is split into 3 sections. The mistake and typos pointed out are correcte

Two-loop perturbative corrections to the constrained effective potential in thermal QCD

In this paper, we compute the constrained QCD effective potential up to two-loop order with finite quark mass and chemical potential. We present the explicit calculations by using the double line notation and analytical expressions for massless quarks are obtained in terms of the Bernoulli polynomials or Polyakov loops. Our results explicitly show that the constrained QCD effective potential is independent on the gauge fixing parameter. In addition, as compared to the massless case, the constrained QCD effective potential with massive quarks develops a completely new term which is only absent when the background field vanishes. Furthermore, we discuss the relation between the one- and two-loop constrained effective potential. The surprisingly simple proportionality that exists in the pure gauge theories, however, is in general no longer true when fermions are taken into account. On the other hand, for high baryon density $\mu_B$ and low temperature $T$, in the massless limit, we do also find a similar proportionality between the one- and two-loop fermionic contributions in the constrained effective potential up to ${\cal O}(T/\mu_B)$.Comment: 36 pages, 5 figs, final version in JHE

Constraints on inflation revisited: An analysis including the latest local measurement of the Hubble constant

We revisit the constraints on inflation models by using the current cosmological observations involving the latest local measurement of the Hubble constant ($H_{0} = 73.00\pm 1.75$ km s $^{-1}$ Mpc$^{-1}$). We constrain the primordial power spectra of both scalar and tensor perturbations with the observational data including the Planck 2015 CMB full data, the BICEP2 and Keck Array CMB B-mode data, the BAO data, and the direct measurement of $H_0$. In order to relieve the tension between the local determination of the Hubble constant and the other astrophysical observations, we consider the additional parameter $N_{\rm eff}$ in the cosmological model. We find that, for the $\Lambda$CDM+$r$+$N_{\rm eff}$ model, the scale invariance is only excluded at the 3.3$\sigma$ level, and $\Delta N_{\rm eff}>0$ is favored at the 1.6$\sigma$ level. Comparing the obtained 1$\sigma$ and 2$\sigma$ contours of $(n_s,r)$ with the theoretical predictions of selected inflation models, we find that both the convex and concave potentials are favored at 2$\sigma$ level, the natural inflation model is excluded at more than 2$\sigma$ level, the Starobinsky $R^2$ inflation model is only favored at around 2$\sigma$ level, and the spontaneously broken SUSY inflation model is now the most favored model.Comment: 10 pages, 6 figure

Constraining dark energy with Hubble parameter measurements: an analysis including future redshift-drift observations

Dark energy affects the Hubble expansion rate (namely, the expansion history) $H(z)$ by an integral over $w(z)$. However, the usual observables are the luminosity distances or the angular diameter distances, which measure the distance-redshift relation. Actually, dark energy affects the distances (and the growth factor) by a further integration over functions of $H(z)$. Thus, the direct measurements of the Hubble parameter $H(z)$ at different redshifts are of great importance for constraining the properties of dark energy. In this paper, we show how the typical dark energy models, for example, the $\Lambda$CDM, $w$CDM, CPL, and holographic dark energy (HDE) models, can be constrained by the current direct measurements of $H(z)$ (31 data in total, covering the redshift range of $z\in [0.07,2.34]$). In fact, the future redshift-drift observations (also referred to as the Sandage-Loeb test) can also directly measure $H(z)$ at higher redshifts, covering the range of $z\in [2,5]$. We thus discuss what role the redshift-drift observations can play in constraining dark energy with the Hubble parameter measurements. We show that the constraints on dark energy can be improved greatly with the $H(z)$ data from only a 10-year observation of redshift drift.Comment: 20 pages, 5 figures; final version published in EPJ

The heavy-quark potential in an anisotropic plasma

We determine the hard-loop resummed propagator in an anisotropic QCD plasma in general covariant gauges and define a potential between heavy quarks from the Fourier transform of its static limit. We find that there is stronger attraction on distance scales on the order of the inverse Debye mass for quark pairs aligned along the direction of anisotropy than for transverse alignment.Comment: 8 pages, 2 figures, final version to appear in PLB, 1 reference added, numerical constant in Eq.(10) correcte