1264030
Elliptic Gaudin models and elliptic KZ equations
The Gaudin models based on the face-type elliptic quantum groups and the XYZ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding face-type Knizhnik–Zamolodchikov equations and their solutions are given.
17047722
Infinite Families of Gauge-Equivalent R-Matrices and Gradations of Quantized Affine Algebras
Associated with the fundamental representation of a quantum algebra such as Uq(A1) or Uq(A2), there exist infinitely many gauge-equivalent R-matrices with different spectralparameter dependences. It is shown how these can be obtained by examining the infinitely many possible gradations of the corresponding quantum affine algebras, such as and , and explicit formulae are obtained for those two cases. Spectral-dependent similarity (gauge) transformations relate the R-matrices in different gradations, Nevertheless, the choice of gradation can be physically significant, as is illustrated in the case of quantum affine Toda field theories.
14103118
Integrable electron model with correlated hopping and quantum supersymmetry
Abstract We give the q -deformed analogue of a recently introduced electron model which generalizes the Hubbard model with additional correlated hopping terms and electron pair hopping. The model contains two independent parameters and is invariant with respect to the quantum superalgebra U q ( gl (2|1)). It is shown to be integrable in one dimension by means of the quantum inverse scattering method.
121731174
Some algebraic identities in anomalous gauge theories
Some useful algebraic relations between the anomaly of Dmu Jmu and anomalous commutators are derived using only the canonical commutators and the equation of motion. Their applications are discussed.
119694191
Construction of basis vectors for symmetric irreducible representations of O(5) $ \supset$ O(3)
Abstract.A recursive method for the construction of symmetric irreducible representations of $ O(2l+1)$ in the $ O(2l+1)\supset O(3)$ basis for identical boson systems is proposed. The formalism is realized based on the group chain $ U(2l+1)\supset U(2l-1)\otimes U(2)$ , of which the symmetric irreducible representations are simply reducible. The basis vectors for symmetric irreducible representations of the $ O(2l+1)\supset O(2l-1)\otimes U(1)$ can easily be constructed from those of U(2l + 1) $ \supset$U(2l - 1) ⊗ U(2) $ \supset$O(2l - 1) ⊗ U(1) with no l -boson pairs, namely with the total boson number exactly equal to the seniority number in the system, from which one can construct symmetric irreducible representations of $ O(2l+1)$ in the $ O(2l-1)\otimes U(1)$ basis when all symmetric irreducible representations of O(2l - 1) are known. As a starting point, basis vectors of symmetric irreducible representations of O(5) are constructed in the $ O_{1}(3)\otimes U(1)$ basis, where $ O_{1}(3)\equiv O(2l-1)$ , when l = 2 , which is generated not by the angular momentum operators of the d -boson system, but by the operators constructed from d -boson creation (annihilation) operators $ d^{\dagger}_{\mu}$ ( $ d_{\mu}$ with $ \mu=1$ , 0, -1 . Matrix representations of $ O(5)\supset O_{1}(3)\otimes U(1)$ , together with the elementary Wigner coefficients, are presented. After the angular momentum projection, a three-term relation in determining the expansion coefficients of the $ O(5)\supset O(3)$ basis vectors, where the O(3) group is generated by the angular momentum operators of the d -boson system, in terms of those of $ O_{1}(3)\otimes U(1)$ is derived. The eigenvectors of the projection matrix with zero eigenvalues constructed according to the three-term relation completely determine the basis vectors of $ O(5)\supset O(3)$ . Formulae for evaluating the elementary Wigner coefficients of $ O(5)\supset O(3)$ are derived explicitly. Analytical expressions of some elementary Wigner coefficients of $ O(5)\supset O(3)$ for the coupling $ (\tau 0)\otimes(1 0)$ with resultant angular momentum quantum number L = 2$ \tau$ + 2 - k for $ k=0,2,3,\ldots,6$ with a multiplicity 2 case for k = 6 are presented.
2107479
Local Quasitriangular Hopf Algebras
We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. The category of modules with finite cycles over a local quasitriangular Hopf algebra is a braided tensor category.
118697431
A naturally light sterile neutrino in an asymmetric dark matter model
A bstractA recently proposed asymmetric mirror dark matter model where the mirror sector is connected with the visible one by a right-handed neutrino portal, is shown to lead naturally to a 3+1 active-sterile neutrino spectrum, if the portal consists only of two right-handed neutrinos. At tree level the model has four massless neutrino states, three (predominately) active and one sterile. The active neutrinos pick up tiny masses via the minimal radiative inverse seesaw mechanism at one-loop level. The loop effects also generate the large solar and atmospheric mixings, as well as the observed reactor mixing for certain ranges of parameters of the model. The dominant contribution to the sterile neutrino mass (~eV) arises from the gravitationally induced dimension-5 operators. Generating active-sterile mixing requires a two Higgs doublet extension of the standard model and a small mixing between the ordinary and mirror Higgs fields, which occurs naturally in mirror models.
118570774
Incompressible Navier-Stokes Equations from Einstein Gravity with Chern-Simons Term
In (2 + 1)-dimensional hydrodynamic systems with broken parity, the shear and bulk viscosity is joined by the Hall viscosity and curl viscosity. The dual holographic model has been constructed by coupling a pseudoscalar to the gravitational Chern-Simons term in (3 + 1)-dimensional bulk gravity. In this paper, we investigate the nonrelativistic fluid with Hall viscosity and curl viscosity living on a finite radial cutoff surface in the bulk. Employing the nonrelativistic hydrodynamic expansion method, we obtain the incompressible Navier-Stokes equations with Hall viscosity and curl viscosity. Unlike the shear viscosity, the ratio of the Hall viscosity over entropy density is found to be cutoff scale dependent, and it tends to zero when the cutoff surface approaches the horizon of the background space-time.
35611437
Top quark forward-backward asymmetry in the little Higgs model
A sizable difference in top quark pair forward backward asymmetry (AFB) is observed at Tevatron. The discrepancy triggers many new physics beyond the standard model (SM) and then constrains the parameter spaces in them. In this article we calculate the AFB of the top-pair production at Tevatron up to next to leading order (NLO) in the little Higgs model (LHM). We find that the contribution of ZH can be large enough to make up the gap between SM prediction and experimental data. Then, the parameter space for the couplings between ZH and quarks are constrained. Thus, this model can fulfill the experimental data, both in AFB and in cross section.
119108763
Magnetic field effect on the phase transition in AdS soliton spacetime
We investigate the scalar perturbations in an anti-de Sitter soliton background coupled to a Maxwell field via marginally stable modes. In the probe limit, we study the magnetic field effect on the holographic insulator/superconductor phase transition numerically and analytically. The condensate will be localized in a finite circular region for any finite constant magnetic field. Near the critical point, we find that there exists a simple relation among the critical chemical potential, magnetic field, the charge, and mass of the scalar field. This relation indicates that the presence of the magnetic field causes the transition from insulator to superconductor to be difficult.
55038482
Scalar suppression on large scales in open inflation
We consider two toy models of open inflation and investigate their ability to give a suppression of scalar power on large scales while also satisfying observational constraints on the spatial curvature of the Universe. Qualitatively we find that both models are indeed capable of fulfilling these two requirements, but we also see that effects of the quantum tunneling must be carefully taken into account if we wish to make quantitative predictions.