Duality and Symmetry in Chiral Potts Model

We discover an Ising-type duality in the general $N$-state chiral Potts model, which is the Kramers-Wannier duality of planar Ising model when N=2. This duality relates the spectrum and eigenvectors of one chiral Potts model at a low temperature (of small $k'$) to those of another chiral Potts model at a high temperature (of $k'^{-1}$). The $\tau^{(2)}$-model and chiral Potts model on the dual lattice are established alongside the dual chiral Potts models. With the aid of this duality relation, we exact a precise relationship between the Onsager-algebra symmetry of a homogeneous superintegrable chiral Potts model and the $sl_2$-loop-algebra symmetry of its associated spin-$\frac{N-1}{2}$ XXZ chain through the identification of their eigenstates.Comment: Latex 34 pages, 2 figures; Typos and misprints in Journal version are corrected with minor changes in expression of some formula

On τ(2)\tau^{(2)}-model in Chiral Potts Model and Cyclic Representation of Quantum Group Uq(sl2)U_q(sl_2)

We identify the precise relationship between the five-parameter $\tau^{(2)}$-family in the $N$-state chiral Potts model and XXZ chains with $U_q (sl_2)$-cyclic representation. By studying the Yang-Baxter relation of the six-vertex model, we discover an one-parameter family of $L$-operators in terms of the quantum group $U_q (sl_2)$. When $N$ is odd, the $N$-state $\tau^{(2)}$-model can be regarded as the XXZ chain of $U_{\sf q} (sl_2)$ cyclic representations with ${\sf q}^N=1$. The symmetry algebra of the $\tau^{(2)}$-model is described by the quantum affine algebra $U_{\sf q} (\hat{sl}_2)$ via the canonical representation. In general for an arbitrary $N$, we show that the XXZ chain with a $U_q (sl_2)$-cyclic representation for $q^{2N}=1$ is equivalent to two copies of the same $N$-state $\tau^{(2)}$-model.Comment: Latex 11 pages; Typos corrected, Minor changes for clearer presentation, References added and updated-Journal versio

The Q-operator for Root-of-Unity Symmetry in Six Vertex Model

We construct the explicit $Q$-operator incorporated with the $sl_2$-loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the $Q$-operator, the six-vertex transfer matrix and fusion matrices are derived from the Bethe equation, parallel to the Onsager-algebra-symmetry discussion in the superintegrable $N$-state chiral Potts model. We show that the whole set of functional equations is valid for the $Q$-operator. Direct calculations in certain cases are also given here for clearer illustration about the nature of the $Q$-operator in the symmetry study of root-of-unity six-vertex model from the functional-relation aspect.Comment: Latex 26 Pages; Typos and small errors corrected, Some explanations added for clearer presentation, References updated-Journal version with modified labelling of sections and formula

Fusion Operators in the Generalized τ(2)\tau^{(2)}-model and Root-of-unity Symmetry of the XXZ Spin Chain of Higher Spin

We construct the fusion operators in the generalized $\tau^{(2)}$-model using the fused $L$-operators, and verify the fusion relations with the truncation identity. The algebraic Bethe ansatz discussion is conducted on two special classes of $\tau^{(2)}$ which include the superintegrable chiral Potts model. We then perform the parallel discussion on the XXZ spin chain at roots of unity, and demonstrate that the $sl_2$-loop-algebra symmetry exists for the root-of-unity XXZ spin chain with a higher spin, where the evaluation parameters for the symmetry algebra are identified by the explicit Fabricius-McCoy current for the Bethe states. Parallels are also drawn to the comparison with the superintegrable chiral Potts model.Comment: Latex 33 Pages; Typos and errors corrected, New improved version by adding explanations for better presentation. Terminology in the content and the title refined. References added and updated-Journal versio

The structure of quotients of the Onsager algebra by closed ideals

We study the Onsager algebra from the ideal theoretic point of view. A complete classification of closed ideals and the structure of quotient algebras are obtained. We also discuss the solvable algebra aspect of the Onsager algebra through the use of formal Lie algebras.Comment: 33 pages, Latex, small topos corrected-Journal versio

Generalized Borcea-Voisin Construction

C. Voisin and C. Borcea have constructed mirror pairs of families of Calabi-Yau threefolds by taking the quotient of the product of an elliptic curve with a K3 surface endowed with a non-symplectic involution. In this paper, we generalize the construction of Borcea and Voisin to any prime order and build three and four dimensional Calabi-Yau orbifolds. We classify the topological types that are obtained and show that, in dimension 4, orbifolds built with an involution admit a crepant resolution and come in topological mirror pairs. We show that for odd primes, there are generically no minimal resolutions and the mirror pairing is lost.Comment: 15 pages, 2 figures. v2: typos corrected & references adde

A deformed analogue of Onsager's symmetry in the XXZ open spin chain

The XXZ open spin chain with general integrable boundary conditions is shown to possess a q-deformed analogue of the Onsager's algebra as fundamental non-abelian symmetry which ensures the integrability of the model. This symmetry implies the existence of a finite set of independent mutually commuting nonlocal operators which form an abelian subalgebra. The transfer matrix and local conserved quantities, for instance the Hamiltonian, are expressed in terms of these nonlocal operators. It follows that Onsager's original approach of the planar Ising model can be extended to the XXZ open spin chain.Comment: 12 pages; LaTeX file with amssymb; v2: typos corrected, clarifications in the text; v3: minor changes in references, version to appear in JSTA

Topological Orbifold Models and Quantum Cohomology Rings

We discuss the toplogical sigma model on an orbifold target space. We describe the moduli space of classical minima for computing correlation functions involving twisted operators, and show, through a detailed computation of an orbifold of ${\bf CP}^1$ by the dihedral group $D_{4},$ how to compute the complete ring of observables. Through this procedure, we compute all the rings from dihedral ${\bf CP}^1$ orbifolds; we note a similarity with rings derived from perturbed $D-$series superpotentials of the $A-D-E$ classification of $N = 2$ minimal models. We then consider ${\bf CP}^2/D_4,$ and show how the techniques of topological-anti-topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds.Comment: 48 pages, harvmac, HUTP-92/A06

Tissue memory CD4+ T cells expressing IL-7 receptor-alpha (CD127) preferentially support latent HIV-1 infection.

The primary reservoir for HIV is within memory CD4+ T cells residing within tissues, yet the features that make some of these cells more susceptible than others to infection by HIV is not well understood. Recent studies demonstrated that CCR5-tropic HIV-1 efficiently enters tissue-derived memory CD4+ T cells expressing CD127, the alpha chain of the IL7 receptor, but rarely completes the replication cycle. We now demonstrate that the inability of HIV to replicate in these CD127-expressing cells is not due to post-entry restriction by SAMHD1. Rather, relative to other memory T cell subsets, these cells are highly prone to undergoing latent infection with HIV, as revealed by the high levels of integrated HIV DNA in these cells. Host gene expression profiling revealed that CD127-expressing memory CD4+ T cells are phenotypically distinct from other tissue memory CD4+ T cells, and are defined by a quiescent state with diminished NFκB, NFAT, and Ox40 signaling. However, latently-infected CD127+ cells harbored unspliced HIV transcripts and stimulation of these cells with anti-CD3/CD28 reversed latency. These findings identify a novel subset of memory CD4+ T cells found in tissue and not in blood that are preferentially targeted for latent infection by HIV, and may serve as an important reservoir to target for HIV eradication efforts

Reduced adipose tissue oxygenation in human obesity evidence for rarefaction, macrophage chemotaxis, and inflammation without an angiogenic response

OBJECTIVE-Based on rodent studies, we examined the hypothesis that increased adipose tissue (AT) mass in obesity without an adequate support of vascularization might lead to hypoxia, macrophage infiltration, and inflammation. RESEARCH DESIGN AND METHODS-Oxygen partial pressure (AT pO 2) and AT temperature in abdominal AT (9 lean and 12 overweight/obese men and women) was measured by direct insertion of a polarographic Clark electrode. Body composition was measured by dual-energy X-ray absorptiometry, and insulin sensitivity was measured by hyperinsulinemic-euglycemic clamp. Abdominal subcutaneous tissue was used for staining, quantitative RT-PCR, and chemokine secretion assay. RESULTS-AT pO 2 was lower in overweight/obese subjects than lean subjects (47 ± 10.6 vs. 55 ± 9.1 mmHg); however, this level of pO 2 did not activate the classic hypoxia targets (pyruvate dehydrogenase kinase and vascular endothelial growth factor [VEGF]). AT pO 2 was negatively correlated with percent body fat (R =-0.50, P \u3c 0.05). Compared with lean subjects, overweight/ obese subjects had 44% lower capillary density and 58% lower VEGF, suggesting AT rarefaction (capillary drop out). This might be due to lower peroxisome proliferator-activated receptor γ1 and higher collagen VI mRNA expression, which correlated with AT pO 2 (P \u3c 0.05). Of clinical importance, AT pO 2 negatively correlated with CD68 mRNA and macrophage inflammatory protein 1α secretion (R =-0.58, R =-0.79, P \u3c 0.05), suggesting that lower AT pO 2 could drive AT inflammation in obesity. CONCLUSIONS-Adipose tissue rarefaction might lie upstream of both low AT pO 2 and inflammation in obesity. These results suggest novel approaches to treat the dysfunctional AT found in obesity. © 2009 by the American Diabetes Association