Cosmic age problem revisited in the holographic dark energy model

Because of an old quasar APM 08279+5255 at $z=3.91$, some dark energy models face the challenge of the cosmic age problem. It has been shown by Wei and Zhang [Phys. Rev. D {\bf 76}, 063003 (2007)] that the holographic dark energy model is also troubled with such a cosmic age problem. In order to accommodate this old quasar and solve the age problem, we propose in this Letter to consider the interacting holographic dark energy in a non-flat universe. We show that the cosmic age problem can be eliminated when the interaction and spatial curvature are both involved in the holographic dark energy model.Comment: 7 pages, 3 figures; v2: typos corrected, version for publication in Phys.Lett.B; v3: typos in eqs (17,18) correcte

Higher loop corrections to a Schwinger--Dyson equation

We consider the effects of higherloop corrections to a Schwinger--Dyson equations for propagators. This is made possible by the efficiency of the methods we developed in preceding works, still using the supersymmetric Wess--Zumino model as a laboratory. We obtain the dominant contributions of the three and four loop primitive divergences at high order in perturbation theory, without the need for their full evaluations. Our main conclusion is that the asymptotic behavior of the perturbative series of the renormalization function remains unchanged, and we conjecture that this will remain the case for all finite order corrections.Comment: 12 pages, 2 imbedded TiKZ pictures. A few clarifications matching the published versio

Spectral extension of the quantum group cotangent bundle

The structure of a cotangent bundle is investigated for quantum linear groups GLq(n) and SLq(n). Using a q-version of the Cayley-Hamilton theorem we construct an extension of the algebra of differential operators on SLq(n) (otherwise called the Heisenberg double) by spectral values of the matrix of right invariant vector fields. We consider two applications for the spectral extension. First, we describe the extended Heisenberg double in terms of a new set of generators -- the Weyl partners of the spectral variables. Calculating defining relations in terms of these generators allows us to derive SLq(n) type dynamical R-matrices in a surprisingly simple way. Second, we calculate an evolution operator for the model of q-deformed isotropic top introduced by A.Alekseev and L.Faddeev. The evolution operator is not uniquely defined and we present two possible expressions for it. The first one is a Riemann theta function in the spectral variables. The second one is an almost free motion evolution operator in terms of logarithms of the spectral variables. Relation between the two operators is given by a modular functional equation for Riemann theta function.Comment: 38 pages, no figure

SUq(2)SU_q(2) Lattice Gauge Theory

We reformulate the Hamiltonian approach to lattice gauge theories such that, at the classical level, the gauge group does not act canonically, but instead as a Poisson-Lie group. At the quantum level, it then gets promoted to a quantum group gauge symmetry. The theory depends on two parameters - the deformation parameter $\lambda$ and the lattice spacing $a$. We show that the system of Kogut and Susskind is recovered when $\lambda \rightarrow 0$, while QCD is recovered in the continuum limit (for any $\lambda$). We thus have the possibility of having a two parameter regularization of QCD.Comment: 26 pages, LATEX fil

Braidings of Tensor Spaces

Let $V$ be a braided vector space, that is, a vector space together with a solution $\hat{R}\in {\text{End}}(V\otimes V)$ of the Yang--Baxter equation. Denote $T(V):=\bigoplus_k V^{\otimes k}$. We associate to $\hat{R}$ a solution $T(\hat{R})\in {\text{End}}(T(V)\otimes T(V))$ of the Yang--Baxter equation on the tensor space $T(V)$. The correspondence $\hat{R}\rightsquigarrow T(\hat{R})$ is functorial with respect to $V$.Comment: 10 pages, no figure

Deformed Traces and Covariant Quantum Algebras for Quantum Groups GLqp(2)GL_{qp}(2) and GLqp(1∣1)GL_{qp}(1|1)

The q-deformed traces and orbits for the two parametric quantum groups $GL_{qp}(2)$ and $GL_{qp}(1|1)$ are defined. They are subsequently used in the construction of $q$-orbit invariants for these groups. General $qp$-(super)oscillator commutation relations are obtained which remain invariant under the coactions of groups $GL_{qp}(2)$ and $GL_{qp}(1|1)$. The $GL_{qp}(2)$ covariant deformed algebra is deduced in terms of the bilinears of bosonic $qp$-oscillators which turns out to be a central extension of the Witten-type deformation of $sl(2)$ algebra. In the case of the supergroup $GL_{qp}(1|1)$, the corresponding covariant algebras contain $N = 2$ supersymmetric quantum mechanical subalgebras.Comment: LaTeX, 11 pages, a note and a reference added, relevant to hep-th/030912

Quantum Group Gauge Theories and Covariant Quantum Algebras

The algebraic formulation of the quantum group gauge models in the framework of the $R$-matrix approach to the theory of quantum groups is given. We consider gauge groups taking values in the quantum groups and noncommutative gauge fields transformed as comodules under the coaction of the gauge quantum group $G_{q}$. Using this approach we construct the quantum deformations of the topological Chern-Simons models, non-abelian gauge theories and the Einstein gravity. The noncommutative fields in these models generate $G_{q}$-covariant quantum algebras.Comment: 12 pages, LaTeX, JINR preprint E2-93-54, Dubna (19 February 1993

On the idempotents of Hecke algebras

We give a new construction of primitive idempotents of the Hecke algebras associated with the symmetric groups. The idempotents are found as evaluated products of certain rational functions thus providing a new version of the fusion procedure for the Hecke algebras. We show that the normalization factors which occur in the procedure are related to the Ocneanu--Markov trace of the idempotents.Comment: 11 page

Feigin-Frenkel center in types B, C and D

For each simple Lie algebra g consider the corresponding affine vertex algebra V_{crit}(g) at the critical level. The center of this vertex algebra is a commutative associative algebra whose structure was described by a remarkable theorem of Feigin and Frenkel about two decades ago. However, only recently simple formulas for the generators of the center were found for the Lie algebras of type A following Talalaev's discovery of explicit higher Gaudin Hamiltonians. We give explicit formulas for generators of the centers of the affine vertex algebras V_{crit}(g) associated with the simple Lie algebras g of types B, C and D. The construction relies on the Schur-Weyl duality involving the Brauer algebra, and the generators are expressed as weighted traces over tensor spaces and, equivalently, as traces over the spaces of singular vectors for the action of the Lie algebra sl_2 in the context of Howe duality. This leads to explicit constructions of commutative subalgebras of the universal enveloping algebras U(g[t]) and U(g), and to higher order Hamiltonians in the Gaudin model associated with each Lie algebra g. We also introduce analogues of the Bethe subalgebras of the Yangians Y(g) and show that their graded images coincide with the respective commutative subalgebras of U(g[t]).Comment: 29 pages, constructions of Pfaffian-type Sugawara operators and commutative subalgebras in universal enveloping algebras are adde

The cohomology of superspace, pure spinors and invariant integrals

The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are discussed and some further theoretical developments presented. The method is applied to higher-order corrections in heterotic string theory up to \a'^3. Some partial results on $N=2,d=10$ and $N=1,d=11$ are also given.Comment: 24 pages. Minor changes; added reference