Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain

We construct the Baxter Q-operator and the representation of the Separated Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the diagrammatical approach, we calculate Sklyanin's integration measure in the separated variables and obtain the solution to the spectral problem for the model in terms of the eigenvalues of the Q-operator. We show that the transition kernel to the SoV representation is factorized into the product of certain operators each depending on a single separated variable. As a consequence, it has a universal pyramid-like form that has been already observed for various quantum integrable models such as periodic Toda chain, closed SL(2,R) and SL(2,C) spin chains.Comment: 29 pages, 9 figures, Latex styl

Separation of variables for the quantum SL(2,R) spin chain

We construct representation of the Separated Variables (SoV) for the quantum SL(2,R) Heisenberg closed spin chain and obtain the integral representation for the eigenfunctions of the model. We calculate explicitly the Sklyanin measure defining the scalar product in the SoV representation and demonstrate that the language of Feynman diagrams is extremely useful in establishing various properties of the model. The kernel of the unitary transformation to the SoV representation is described by the same "pyramid diagram" as appeared before in the SoV representation for the SL(2,C) spin magnet. We argue that this kernel is given by the product of the Baxter Q-operators projected onto a special reference state.Comment: 26 pages, Latex style, 9 figures. References corrected, minor stylistic changes, version to be publishe

High Energy QCD: Stringy Picture from Hidden Integrability

We discuss the stringy properties of high-energy QCD using its hidden integrability in the Regge limit and on the light-cone. It is shown that multi-colour QCD in the Regge limit belongs to the same universality class as superconformal $\cal{N}$=2 SUSY YM with $N_f=2N_c$ at the strong coupling orbifold point. The analogy with integrable structure governing the low energy sector of $\cal{N}$=2 SUSY gauge theories is used to develop the brane picture for the Regge limit. In this picture the scattering process is described by a single M2 brane wrapped around the spectral curve of the integrable spin chain and unifying hadrons and reggeized gluons involved in the process. New quasiclassical quantization conditions for the complex higher integrals of motion are suggested which are consistent with the $S-$duality of the multi-reggeon spectrum. The derivation of the anomalous dimensions of the lowest twist operators is formulated in terms of the Riemann surfacesComment: 37 pages, 3 figure

Instantons and Yang-Mills Flows on Coset Spaces

We consider the Yang-Mills flow equations on a reductive coset space G/H and the Yang-Mills equations on the manifold R x G/H. On nonsymmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin connection. The condition of G-equivariance imposed on the gauge fields reduces the Yang-Mills equations to phi^4-kink equations on R. Depending on the boundary conditions and torsion, we obtain solutions to the Yang-Mills equations describing instantons, chains of instanton-anti-instanton pairs or modifications of gauge bundles. For Lorentzian signature on R x G/H, dyon-type configurations are constructed as well. We also present explicit solutions to the Yang-Mills flow equations and compare them with the Yang-Mills solutions on R x G/H.Comment: 1+12 page

Bounds on the tau and muon neutrino vector and axial vector charge radius

A Majorana neutrino is characterized by just one flavor diagonal electromagnetic form factor: the anapole moment, that in the static limit corresponds to the axial vector charge radius . Experimental information on this quantity is scarce, especially in the case of the tau neutrino. We present a comprehensive analysis of the available data on the single photon production process $e^+ e^- -> \nu \bar\nu \gamma$ off Z-resonance, and we discuss the constraints that these measurements can set on for the tau neutrino. We also derive limits for the Dirac case, when the presence of a vector charge radius is allowed. Finally, we comment on additional experimental data on $\nu_\mu$ scattering from the NuTeV, E734, CCFR and CHARM-II collaborations, and estimate the limits implied for and for the muon neutrino.Comment: 20 pages, 2 eps figures. CCFR data included in the analysis. Conclusion unchange

Relationships between Substrate Promiscuity and Chiral Selectivity of Esterases from Phylogenetically and Environmentally Diverse Microorganisms

Substrate specificity and selectivity of a biocatalyst are determined by the protein sequence and structure of its active site. Finding versatile biocatalysts acting against multiple substrates while at the same time being chiral selective is of interest for the pharmaceutical and chemical industry. However, the relationships between these two properties in natural microbial enzymes remain underexplored. Here, we performed an experimental analysis of substrate promiscuity and chiral selectivity in a set of 145 purified esterases from phylogenetically and environmentally diverse microorganisms, which were assayed against 96 diverse esters, 20 of which were enantiomers. Our results revealed a negative correlation between substrate promiscuity and chiral selectivity in the evaluated enzymes. Esterases displaying prominent substrate promiscuity and large catalytic environments are characterized by low chiral selectivity, a feature that has limited commercial value. Although a low level of substrate promiscuity does not guarantee high chiral selectivity, the probability that esterases with smaller active sites possess chiral selectivity factors of interest for industry (>25) is significantly higher than for promiscuous enzymes. Together, the present study unambiguously demonstrates that promiscuous and selective esterases appear to be rare in nature and that substrate promiscuity can be used as an indicator of the chiral selectivity level of esterases, and vice versa

Numerical analysis of the radio-frequency single-electron transistor operation

We have analyzed numerically the response and noise-limited charge sensitivity of a radio-frequency single-electron transistor (RF-SET) in a non-superconducting state using the orthodox theory. In particular, we have studied the performance dependence on the quality factor Q of the tank circuit for Q both below and above the value corresponding to the impedance matching between the coaxial cable and SET.Comment: 14 page

Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons

We consider a complex vector bundle E endowed with a connection A over the eight-dimensional manifold R^2 x G/H, where G/H = SU(3)/U(1)xU(1) is a homogeneous space provided with a never integrable almost complex structure and a family of SU(3)-structures. We establish an equivalence between G-invariant solutions A of the Spin(7)-instanton equations on R^2 x G/H and general solutions of non-Abelian coupled vortex equations on R^2. These vortices are BPS solitons in a d=4 gauge theory obtained from N=1 supersymmetric Yang-Mills theory in ten dimensions compactified on the coset space G/H with an SU(3)-structure. The novelty of the obtained vortex equations lies in the fact that Higgs fields, defining morphisms of vector bundles over R^2, are not holomorphic in the generic case. Finally, we introduce BPS vortex equations in N=4 super Yang-Mills theory and show that they have the same feature.Comment: 14 pages; v2: typos fixed, published versio

Crossover and scaling in a nearly antiferromagnetic Fermi liquid in two dimensions

We consider two-dimensional Fermi liquids in the vicinity of a quantum transition to a phase with commensurate, antiferromagnetic long-range order. Depending upon the Fermi surface topology, mean-field spin-density-wave theory predicts two different types of such transitions, with mean-field dynamic critical exponents $z=1$ (when the Fermi surface does not cross the magnetic zone boundary, type $A$) and $z=2$ (when the Fermi surface crosses the magnetic zone boundary, type $B$). The type $A$ system only displays $z=1$ behavior at all energies and its scaling properties are similar (though not identical) to those of an insulating Heisenberg antiferromagnet. Under suitable conditions precisely stated in this paper, the type $B$ system displays a crossover from relaxational behavior at low energies to type $A$ behavior at high energies. A scaling hypothesis is proposed to describe this crossover: we postulate a universal scaling function which determines the entire, temperature-, wavevector-, and frequency-dependent, dynamic, staggered spin susceptibility in terms of 4 measurable, $T=0$, parameters (determining the distance, energy, and order parameter scales, plus one crossover parameter). The scaling function contains the full scaling behavior in all regimes for both type $A$ and $B$ systems. The crossover behavior of the uniform susceptibility and the specific heat is somewhat more complicated and is also discussed. Explicit computation of the crossover functions is carried out in a large $N$ expansion on a mean-field model. Some new results for the critical properties on the ordered side of the transition are also obtained in a spin-density wave formalism. The possible relevance of our results to the doped cuprate compounds is briefly discussed.Comment: 20 pages, REVTeX, 6 figures (uuencoded compressed PostScript file for figures is appended

Collective cancer invasion forms an integrin-dependent radioresistant niche

Contains fulltext : 219833.pdf (Publisher’s version ) (Open Access)Cancer fatalities result from metastatic dissemination and therapy resistance, both processes that depend on signals from the tumor microenvironment. To identify how invasion and resistance programs cooperate, we used intravital microscopy of orthotopic sarcoma and melanoma xenografts. We demonstrate that these tumors invade collectively and that, specifically, cells within the invasion zone acquire increased resistance to radiotherapy, rapidly normalize DNA damage, and preferentially survive. Using a candidate-based approach to identify effectors of invasion-associated resistance, we targeted beta1 and alphaVbeta3/beta5 integrins, essential extracellular matrix receptors in mesenchymal tumors, which mediate cancer progression and resistance. Combining radiotherapy with beta1 or alphaV integrin monotargeting in invading tumors led to relapse and metastasis in 40-60% of the cohort, in line with recently failed clinical trials individually targeting integrins. However, when combined, anti-beta1/alphaV integrin dual targeting achieved relapse-free radiosensitization and prevented metastatic escape. Collectively, invading cancer cells thus withstand radiotherapy and DNA damage by beta1/alphaVbeta3/beta5 integrin cross-talk, but efficient radiosensitization can be achieved by multiple integrin targeting