13,991 research outputs found
Coverings and Truncations of Graded Selfinjective Algebras
Let be a graded self-injective algebra. We describe its smash
product \Lambda# k\mathbb Z^* with the group , its Beilinson
algebra and their relationship. Starting with , we construct algebras
with finite global dimension, called -slice algebras, we show that their
trivial extensions are all isomorphic, and their repetitive algebras are the
same \Lambda# k\mathbb Z^*. There exist -mutations similar to the BGP
reflections for the -slice algebras. We also recover Iyama's absolute
-complete algebra as truncation of the Koszul dual of certain self-injective
algebra.Comment: Manuscript revised, introduction and abstract rewritte
On -translation algebras
Motivated by Iyama's higher representation theory, we introduce
-translation quivers and -translation algebras. The classical construction of the translation quiver is generalized to construct an
-translation quiver from an -translation quiver, using trivial
extension and smash product. We prove that the quadratic dual of
-translation algebras have -almost splitting sequences in the
category of its projective modules. We also present a non-Koszul
-translation algebra whose trivial extension is -translation algebra,
thus also provides a class of examples of -Koszul algebras (and also a
class of -Koszul algebras) for all .Comment: The paper is revised, according to the referees' suggestions and
comments. The definitions of -translation quiver, admissibility are
rewritten, and the results related to these definition are revised. The
results concerning -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 and low temperature , 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 .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 ( km s Mpc). 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 . In
order to relieve the tension between the local determination of the Hubble
constant and the other astrophysical observations, we consider the additional
parameter in the cosmological model. We find that, for the
CDM++ model, the scale invariance is only excluded at
the 3.3 level, and is favored at the 1.6
level. Comparing the obtained 1 and 2 contours of
with the theoretical predictions of selected inflation models, we find that
both the convex and concave potentials are favored at 2 level, the
natural inflation model is excluded at more than 2 level, the
Starobinsky inflation model is only favored at around 2 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)
by an integral over . 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 . Thus, the
direct measurements of the Hubble parameter 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
CDM, CDM, CPL, and holographic dark energy (HDE) models, can be
constrained by the current direct measurements of (31 data in total,
covering the redshift range of ). In fact, the future
redshift-drift observations (also referred to as the Sandage-Loeb test) can
also directly measure at higher redshifts, covering the range of . 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 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
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