Nonstandard Higgs in Electroweak Chiral Lagrangian

We add a nonstandard higgs into the traditional bosonic part of electroweak chiral Lagrangian, in purpose of finding out the contribution to EWCL coefficients from processes with internal line higgs particle. To construct the effective Lagrangian with higgs, we use low energy expansion scheme and write down all the independent terms conserving $SU(2)\times U_Y(1)$ symmetry in the nonlinear representation which we show is equivalent to the linear representation. Then we integrate out higgs using loop expansion technique at 1-loop level, contributions from all possible terms are obtained. We find three terms, $\mathcal{L}_5$, $\mathcal{L}_7$, $\mathcal{L}_{10}$ in EWCL are important, for which the contributions from higgs can be further expressed in terms of higgs partial decay width $\Gamma_{h\to ZZ}$ and $\Gamma_{h\to WW}$. Higg mass dependence of the coefficients in EWCL are discussed.Comment: 25 pages, 0 figure

Amending the Vafa-Witten Theorem

The strong version of the Vafa-Witten theorem is shown may not to hold because the zero condensate from a direct computation of the order parameter is found to be a result on the symmetric vacuum. The validity of the Vafa-Witten theorem relies then on its weak version, that the Goldstone boson is absent in vector-like gauge theories with vanishing \theta-angle. The existence of a charged \rho-meson condensate, which violates electromagnetic gauge symmetry, is consistent with this weak version of the Vafa-Witten theorem when applied to strong magnetic fields in QCD.Comment: 6 page

Ding-Iohara algebras and quantum vertex algebras

In this paper, we associate quantum vertex algebras to a certain family of associative algebras \widetilde{\A}(g) which are essentially Ding-Iohara algebras. To do this, we introduce another closely related family of associative algebras \A(h). The associated quantum vertex algebras are based on the vacuum modules for \A(h), whereas $\phi$-coordinated modules for these quantum vertex algebras are associated to $\widetilde{A}(g)$-modules. Furthermore, we classify their irreducible $\phi$-coordinated modules.Comment: 33 pages. arXiv admin note: text overlap with arXiv:1505.0716

Multiphonons resonance Raman scattering in Landau-quantized graphene

We theoretically investigate multiphonons resonance Raman scattering between the Landau levels in graphene on the polar substrate using the Huang-Rhys's model. We not only present the single and multiple surface optical (SO) phonons scattering, but also propose the combined multiphonons scattering (CMS), which is composed of the SO phonon and longitudinal acoustic phonon. We find that the CMS has a blue-shift behavior with increasing the magnetic field, differing from these SO phonon resonance scattering at a special magnetic field. This behavior may be used to explain the changing shoulder of the Raman spectrum of optical phonon resonance scattering in experiments. The theoretical model could be expanded to analyze the fine structure of Raman spectrum in two-dimensional materials

M\"obius and Laguerre geometry of Dupin Hypersurfaces

In this paper we show that a Dupin hypersurface with constant M\"{o}bius curvatures is M\"{o}bius equivalent to either an isoparametric hypersurface in the sphere or a cone over an isoparametric hypersurface in a sphere. We also show that a Dupin hypersurface with constant Laguerre curvatures is Laguerre equivalent to a flat Laguerre isoparametric hypersurface. These results solve the major issues related to the conjectures of Cecil et al on the classification of Dupin hypersurfaces.Comment: 45 pages. arXiv admin note: text overlap with arXiv:math/0512090 by other author

On vertex Leibniz algebras

In this paper, we study a notion of what we call vertex Leibniz algebra. This notion naturally extends that of vertex algebra without vacuum, which was previously introduced by Huang and Lepowsky. We show that every vertex algebra without vacuum can be naturally extended to a vertex algebra. On the other hand, we show that a vertex Leibniz algebra can be embedded into a vertex algebra if and only if it admits a faithful module. To each vertex Leibniz algebra we associate a vertex algebra without vacuum which is universal to the forgetful functor. Furthermore, from any Leibniz algebra \g we construct a vertex Leibniz algebra V_{\g} and show that V_{\g} can be embedded into a vertex algebra if and only if \g is a Lie algebra.Comment: latex, 25 page

qq-Virasoro algebra and vertex algebras

In this paper, we study a certain deformation $D$ of the Virasoro algebra that was introduced and called $q$-Virasoro algebra by Nigro,in the context of vertex algebras. Among the main results, we prove that for any complex number $\ell$, the category of restricted $D$-modules of level $\ell$ is canonically isomorphic to the category of quasi modules for a certain vertex algebra of affine type. We also prove that the category of restricted $D$-modules of level $\ell$ is canonically isomorphic to the category of $\mathbb{Z}$-equivariant $\phi$-coordinated quasi modules for the same vertex algebra. In the process, we introduce and employ a certain infinite dimensional Lie algebra which is defined in terms of generators and relations and then identified explicitly with a subalgebra of $\mathfrak{gl}_{\infty}$

Twisted modules for Toroidal vertex algebras

This is a paper in a series systematically to study toroidal vertex algebras. Previously, a theory of toroidal vertex algebras and modules was developed and toroidal vertex algebras were explicitly associated to toroidal Lie algebras. In this paper, we study twisted modules for toroidal vertex algebras. More specifically, we introduce a notion of twisted module for a general toroidal vertex algebra with a finite order automorphism and we give a general construction of toroidal vertex algebras and twisted modules. We then use this construction to establish a natural association of toroidal vertex algebras and twisted modules to twisted toroidal Lie algebras. This together with some other known results implies that almost all extended affine Lie algebras can be associated to toroidal vertex algebras.Comment: 30 page

q-Virasoro algebra and affine Kac-Moody Lie algebras

We establish a natural connection of the $q$-Virasoro algebra $D_{q}$ introduced by Belov and Chaltikian with affine Kac-Moody Lie algebras. More specifically, for each abelian group $S$ together with a one-to-one linear character $\chi$, we define an infinite-dimensional Lie algebra $D_{S}$ which reduces to $D_{q}$ when $S=\mathbb{Z}$. Guided by the theory of equivariant quasi modules for vertex algebras, we introduce another Lie algebra ${\mathfrak{g}}_{S}$ with $S$ as an automorphism group and we prove that $D_{S}$ is isomorphic to the $S$-covariant algebra of the affine Lie algebra $\widehat{{\mathfrak{g}}_{S}}$. We then relate restricted $D_{S}$-modules of level $\ell\in \mathbb{C}$ to equivariant quasi modules for the vertex algebra $V_{\widehat{\mathfrak{g}_{S}}}(\ell,0)$ associated to $\widehat{{\mathfrak{g}}_{S}}$ with level $\ell$. Furthermore, we show that if $S$ is a finite abelian group of order $2l+1$, $D_{S}$ is isomorphic to the affine Kac-Moody algebra of type $B^{(1)}_{l}$.Comment: 20 page

Chiral Quark Model Calculation of the Momentum Dependence of Hadronic Current Correlation Functions at Finite Temperature

We calculate spectral functions associated with hadronic current correlation functions for vector currents at finite temperature. We make use of a model with chiral symmetry, temperature-dependent coupling constants and temperature-dependent momentum cutoff parameters. Our model has two parameters which are used to fix the magnitude and position of the large peak seen in the spectral functions. In our earlier work, good fits were obtained for the spectral functions that were extracted from lattice data by means of the maximum entropy method (MEM). In the present work we extend our calculations and provide values for the three-momentum dependence of the vector correlation function at $T=1.5T_c$. These results are used to obtain the correlation function in coordinate space, which is usually parametrized in terms of a screening mass. Our results for the three-momentum dependence of the spectral functions are similar to those found in a recent lattice QCD calculation for charmonium [S. Datta, F. Karsch, P. Petreczky and I. Wetzorke, hep-lat/0312037]. However, we do not find the expontential behavior in coordinate space that is usually assumed for the spectral function for $T>T_c$ and which allows for the definition of a screening mass.Comment: 16 pages, 5 figures, revtex