17226943
Superconformal Affine Liouville Theory
We present a superconformally invariant and integrable model based on the twisted affine KacMoody superalgebra ˆ osp(2|2) (2) which is the supersymmetrization of the purely bosonic conformal affine Liouville theory recently proposed by Babelon and Bonora. Our model reduces to the super-Liouville or to the super sinh-Gordon theories under certain limit conditions and can be obtained, via hamiltonian reduction, from a superspace WZNW model with values in the corresponding affine KM supergroup. The reconstruction formulae for classical solutions are given. The classical r-matrices in the homogeneous grading and the exchange algebras are worked out. Address after October 1, 1992: Laboratoire de Physique Théorique ENSLAPP, Ecole Normale Supérieure de Lyon, 46 Allée d’Italie, 69007 Lyon, France Address after 28 October 1992: Department of Mathematics, University of Queensland, Brisbane, Qld 4072, Australia
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.
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.
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.
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.
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.
117679007
Measurement of charm production cross-section and leptons from its semileptonic decay at RHIC
In this thesis, we present the measurements of $D^{0}\to K\pi$ at low $p_T$ ($p_T\leq2$ GeV/$c$) and non-photonic electron spectra ($0.9\leq p_T\leq5$ GeV/$c$) from $D^0$ semi-leptonic decay. In addition, we use a newly proposed technique to identify muons from charm decays at low $p_T$. The combination of all these three measurements stringently constrains the total charm production cross-section at mid-rapidity at RHIC. They also allow the extraction of the charmed hadron spectral shape and a study of possible charm radial flow in Au+Au collisions.
119268020
Integrand-level reduction of loop amplitudes by computational algebraic geometry methods
A bstractWe present an algorithm for the integrand-level reduction of multi-loop amplitudes of renormalizable field theories, based on computational algebraic geometry. This algorithm uses (1) the Gröbner basis method to determine the basis for integrand-level reduction, (2) the primary decomposition of an ideal to classify all inequivalent solutions of unitarity cuts. The resulting basis and cut solutions can be used to reconstruct the integrand from unitarity cuts, via polynomial fitting techniques. The basis determination part of the algorithm has been implemented in the Mathematica package, BasisDet. The primary decomposition part can be readily carried out by algebraic geometry softwares, with the output of the package BasisDet. The algorithm works in both D = 4 and D = 4 − 2ϵ dimensions, and we present some two and three-loop examples of applications of this algorithm.
119297362
Holographic forced fluid dynamics in non-relativistic limit
We study the thermodynamics and non-relativistic hydrodynamics of the holographic fluid on a finite cutoff surface in the Gauss-Bonnet gravity. It is shown that the isentropic flow of the fluid is equivalent to a radial component of gravitational field equations. We use the non-relativistic fluid expansion method to study the Einstein-Maxwell-dilaton system with a negative cosmological constant, and obtain the holographic incompressible forced Navier-Stokes equations of the dual fluid at AdS boundary and at a finite cutoff surface, respectively. The concrete forms of external forces are given. (c) 2012 Elsevier B.V. All rights reserved.
119243384
Supernova Cooling in a Dark Matter Smog
A light hidden gauge boson with kinetic mixing with the usual photon is a popular setup in theories of dark matter. The supernova cooling via radiating the hidden boson is known to put an important constraint on the mixing. I consider the possible role dark matter, which under reasonable assumptions naturally exists inside supernova, can play in the cooling picture. Because the interaction between the hidden gauge boson and DM is likely unsuppressed, even a small number of dark matter compared to protons inside the supernova could dramatically shorten the free streaming length of the hidden boson. A picture of a dark matter "smog" inside the supernova, which substantially relaxes the cooling constraint, is discussed in detail.