The Monodromy Matrices of the XXZ Model in the Infinite Volume Limit

We consider the XXZ model in the infinite volume limit with spin half quantum space and higher spin auxiliary space. Using perturbation theory arguments, we relate the half infinite transfer matrices of this class of models to certain $U_q(\hat{sl_2})$ intertwiners introduced by Nakayashiki. We construct the monodromy matrices, and show that the one with spin one auxiliary space gives rise to the L operator.Comment: 19 page

QKZ equation with |q|=1 and correlation functions of the XXZ model in the gapless regime

An integral solution to the quantum Knizhnik-Zamolodchikov ($q$KZ) equation with $|q|=1$ is presented. Upon specialization, it leads to a conjectural formula for correlation functions of the XXZ model in the gapless regime. The validity of this conjecture is verified in special cases, including the nearest neighbor correlator with an arbitrary coupling constant, and general correlators in the XXX and XY limits

Hidden Grassmann structure in the XXZ model V: sine-Gordon model

We study one-point functions of the sine-Gordon model on a cylinder. Our approach is based on a fermionic description of the space of descendent fields, developed in our previous works for conformal field theory and the sine-Gordon model on the plane. In the present paper we make an essential addition by giving a connection between various primary fields in terms of yet another kind of fermions. The one-point functions of primary fields and descendants are expressed in terms of a single function defined via the data from the thermodynamic Bethe Ansatz equations.Comment: 36 pages. Some corrections are done in latest version, especially in the subsection 10.

Mixing of Ground States in Vertex Models

We consider the analogue of the 6-vertex model constructed from alternating spin n/2 and spin m/2 lines, where $1\leq n<m$. We identify the transfer matrix and the space on which it acts in terms of the representation theory of $U_q(sl_2)$. We diagonalise the transfer matrix and compute the S-matrix. We give a trace formula for local correlation functions. When n=1, the 1-point function of a spin m/2 local variable for the alternating lattice with a particular ground state is given as a linear combination of the 1-point functions of the pure spin m/2 model with different ground states. The mixing ratios are calculated exactly and are expressed in terms of irreducible characters of $U_q(sl_2)$ and the deformed Virasoro algebra.Comment: 12 pages, LaTeX, typos correcte

Spectrum of Eleven-dimensional Supergravity on a PP-wave Background

We calculate the spectrum of the linearized supergravity around the maximally supersymmetric pp-wave background in eleven dimensions. The resulting spectrum agrees with that of zero-mode Hamiltonian of a supermembrane theory on the pp-wave background. We also discuss the connection with the Kaluza-Klein zero modes of AdS_4 x S^7 background.Comment: 17 pages, no figures, LaTeX2e, typos correcte

Diagonalization of the XXZ Hamiltonian by Vertex Operators

We diagonalize the anti-ferroelectric XXZ-Hamiltonian directly in the thermodynamic limit, where the model becomes invariant under the action of affine U_q( sl(2) ). Our method is based on the representation theory of quantum affine algebras, the related vertex operators and KZ equation, and thereby bypasses the usual process of starting from a finite lattice, taking the thermodynamic limit and filling the Dirac sea. From recent results on the algebraic structure of the corner transfer matrix of the model, we obtain the vacuum vector of the Hamiltonian. The rest of the eigenvectors are obtained by applying the vertex operators, which act as particle creation operators in the space of eigenvectors. We check the agreement of our results with those obtained using the Bethe Ansatz in a number of cases, and with others obtained in the scaling limit --- the $su(2)$-invariant Thirring model.Comment: 65 page

AdS Vacua, Attractor Mechanism and Generalized Geometries

We consider flux vacua attractor equations in type IIA string theory compactified on generalized geometries with orientifold projections. The four-dimensional N=1 superpotential in this compactification can be written as the sum of the Ramond-Ramond superpotential and a term described by (non)geometric flux charges. We exhibit a simple model in which supersymmetric AdS and Minkowski solutions are classified by means of discriminants of the two superpotentials. We further study various configurations without Ramond-Ramond flux charges. In this case we find supersymmetric AdS vacua both in the case of compactifications on generalized geometries with SU(3) x SU(3) structures and on manifolds with an SU(3)-structure without nongeometric flux charges. In the latter case, we have to introduce correction terms into the prepotential in order to realize consistent vacua.Comment: 35 pages, accepted version in JHE

Divergent Evolution of CHD3 Proteins Resulted in MOM1 Refining Epigenetic Control in Vascular Plants

Arabidopsis MOM1 is required for the heritable maintenance of transcriptional gene silencing (TGS). Unlike many other silencing factors, depletion of MOM1 evokes transcription at selected loci without major changes in DNA methylation or histone modification. These loci retain unusual, bivalent chromatin properties, intermediate to both euchromatin and heterochromatin. The structure of MOM1 previously suggested an integral nuclear membrane protein with chromatin-remodeling and actin-binding activities. Unexpected results presented here challenge these presumed MOM1 activities and demonstrate that less than 13% of MOM1 sequence is necessary and sufficient for TGS maintenance. This active sequence encompasses a novel Conserved MOM1 Motif 2 (CMM2). The high conservation suggests that CMM2 has been the subject of strong evolutionary pressure. The replacement of Arabidopsis CMM2 by a poplar motif reveals its functional conservation. Interspecies comparison suggests that MOM1 proteins emerged at the origin of vascular plants through neo-functionalization of the ubiquitous eukaryotic CHD3 chromatin remodeling factors. Interestingly, despite the divergent evolution of CHD3 and MOM1, we observed functional cooperation in epigenetic control involving unrelated protein motifs and thus probably diverse mechanisms

Three SRA-Domain Methylcytosine-Binding Proteins Cooperate to Maintain Global CpG Methylation and Epigenetic Silencing in Arabidopsis

Methylcytosine-binding proteins decipher the epigenetic information encoded by DNA methylation and provide a link between DNA methylation, modification of chromatin structure, and gene silencing. VARIANT IN METHYLATION 1 (VIM1) encodes an SRA (SET- and RING-associated) domain methylcytosine-binding protein in Arabidopsis thaliana, and loss of VIM1 function causes centromere DNA hypomethylation and centromeric heterochromatin decondensation in interphase. In the Arabidopsis genome, there are five VIM genes that share very high sequence similarity and encode proteins containing a PHD domain, two RING domains, and an SRA domain. To gain further insight into the function and potential redundancy among the VIM proteins, we investigated strains combining different vim mutations and transgenic vim knock-down lines that down-regulate multiple VIM family genes. The vim1 vim3 double mutant and the transgenic vim knock-down lines showed decreased DNA methylation primarily at CpG sites in genic regions, as well as repeated sequences in heterochromatic regions. In addition, transcriptional silencing was released in these plants at most heterochromatin regions examined. Interestingly, the vim1 vim3 mutant and vim knock-down lines gained ectopic CpHpH methylation in the 5S rRNA genes against a background of CpG hypomethylation. The vim1 vim2 vim3 triple mutant displayed abnormal morphological phenotypes including late flowering, which is associated with DNA hypomethylation of the 5′ region of FWA and release of FWA gene silencing. Our findings demonstrate that VIM1, VIM2, and VIM3 have overlapping functions in maintenance of global CpG methylation and epigenetic transcriptional silencing