A conformally broken system as the constrained SL(2,R) WZNW model, its integrability and dressing symmetry
This paper is devoted to the study of the conformally broken system related to the conformally invariant SL(2,R) WZNW model. Our starting point is such an action that is similar in form to the action of gauged WZNW theories developed by Balog et al. (1990). However, the Lagrangian multipliers in our case are assumed to take their values on the mixing of upper and lower Borel subalgebras of sl(2). The system obtained turns out to be an off-conformal extension of the sinh-Gordon model. Its integrability is displayed by the Lax formalism with an arbitrary spectral parameter, the classical r-matrix, and the hidden dressing symmetry.

title: Exact solution of the Izergin-Korepin model with general non-diagonal boundary terms
abstract: A bstractThe Izergin-Korepin model with general non-diagonal boundary terms, a typical integrable model beyond A-type and without U(1)-symmetry, is studied via the offdiagonal Bethe ansatz method. Based on some intrinsic properties of the R-matrix and the K-matrices, certain operator product identities of the transfer matrix are obtained at some special points of the spectral parameter. These identities and the asymptotic behaviors of the transfer matrix together allow us to construct the inhomogeneous T − Q relation and the associated Bethe ansatz equations. In the diagonal boundary limit, the reduced results coincide exactly with those obtained via other methods.

title: Eigenvalues of Ruijsenaars–Schneider models associated with An−1 root system in Bethe ansatz formalism
abstract: Ruijsenaars–Schneider models associated with An−1 root system with a discrete coupling constant are studied. The eigenvalues of the Hamiltonian are given in terms of the Bethe ansatz formulas. Taking the “nonrelativistic” limit, we obtain the spectrum of the corresponding Calogero–Moser systems in the third formulas of Felder et al.

title: Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields
abstract: The anisotropic spin-1/2 chains with arbitrary boundary fields are diagonalized with the off-diagonal Bethe ansatz method. Based on the properties of the R-matrix and the K-matrices, an operator product identity of the transfer matrix is constructed at some special points of the spectral parameter. Combining with the asymptotic behavior (for XXZ case) or the quasi-periodicity properties (for XYZ case) of the transfer matrix, the extended T-Q ansatzes and the corresponding Bethe ansatz equations are derived.

title: Primary fields and screening currents of gl(2|2) non-unitary conformal field theory
abstract: The non-semisimple gl(2)k current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of gl(212) and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields.

title: Drinfeld twists and symmetric Bethe vectors of supersymmetric fermion models
abstract: We construct the Drinfeld twists (factorizing F-matrices) of the gl(m|n)-invariant fermion model. Completely symmetric representation of the pseudo-particle creation operators of the model are obtained in the basis provided by the F-matrix (the F-basis). We resolve the hierarchy of the nested Bethe vectors in the F-basis for the gl(m|n) supersymmetric model.

title: Axial form-factor and induced pseudoscalar form-factor of the nucleons
abstract: We calculate the axial and the induced pseudoscalar form-factors GA(t=-Q2) and GP(t=-Q2) of the nucleons in the framework of the light-cone QCD sum-rules approach up to twist-6 three valence quark light-cone distribution amplitudes, and observe that the form-factors GA(t=-Q2) and GP(t=-Q2) at intermediate and large momentum transfers with Q2>2 GeV2 have significant contributions from the end-point (soft) terms. The numerical values for the axial form-factor GA(t=-Q2) are compatible with the experimental data and theoretical calculations; for example, the chiral quark models and lattice QCD. The numerical values for the induced pseudoscalar form-factor GP(t=-Q2) are compatible with the calculation from the Bethe–Salpeter equation.

title: A New approach for calculating the Nambu-Gorkov propagator in color superconductivity theory
abstract: In this article, we propose a new approach to calculate the Nambu-Gorkov propagator intuitively with some linear algebra techniques in presence of the scalar diquark condensates. With the help of energy projective operators, we can obtain relatively simple expressions for the quark propagators, which greatly facilitate the calculations in solving the Schwinger-Dyson equation to obtain the gap parameters.

title: Fermion masses and flavor mixing in supersymmetric SO(10) model
abstract: We study fermion masses and flavor mixing in a supersymmetric SO ( 10 ) model, where 10, 120 and 126 ¯ Higgs multiplets have Yukawa couplings with matter multiplets and give masses to quarks and leptons through the breaking chain of a Pati–Salam group. This brings about that, at the GUT energy scale, the lepton mass matrices are related to the quark ones via several breaking parameters, and the small neutrino masses arise from a Type II see-saw mechanism. When evolving renormalization group equations for the fermion mass matrices from the GUT scale to the electroweak scale, in a specific parameter scenario, we show that the model can elegantly accommodate all observed values of masses and mixing for the quarks and leptons, especially, it's predictions for the bi-large mixing in the leptonic sector are very well in agreement with the current neutrino experimental data.

title: Grand Canonical Ensembles in General Relativity
abstract: We develop a formalism for general relativistic, grand canonical ensembles in space-times with timelike Killing fields. Using that, we derive ideal gas laws, and show how they depend on the geometry of the particular space-times. A systematic method for calculating Newtonian limits is given for a class of these space-times, which is illustrated for Kerr space-time. In addition, we prove uniqueness of the infinite volume Gibbs measure, and absence of phase transitions for a class of interaction potentials in anti-de Sitter space.

title: A Model of Fermion Masses and Flavor Mixings with Family Symmetry $SU(3)\otimes U(1)$
abstract: The family symmetry SU(3)⊗U(1) is proposed to solve flavor problems about fermion masses and flavor mixings. It’s breaking is implemented by some flavon fields at the high-energy scale. In addition a discrete group Z2 is introduced to generate tiny neutrino masses, which is broken by a real singlet scalar field at the middle-energy scale. The low-energy effective theory is elegantly obtained after all of super-heavy fermions are integrated out and decoupling. All the fermion mass matrices are regularly characterized by four fundamental matrices and thirteen parameters. The model can perfectly fit and account for all the current experimental data about the fermion masses and flavor mixings, in particular, it finely predicts the first generation quark masses and the values of θ l 13 and J l CP in neutrino physics. All of the results are promising to be tested in the future experiments.