119406327
Affine Yang-Mills theory and affine self-dual Chern-Simons Solitons
A four-dimensional affine Yang-Mills theory, i.e. Yang—Mills gauge theory with values in an affine Kac-Moody algebra, is constructed which can give rise to a spontaneous breakdown of the affine symmetry. The affine self-dual Yang-Mills equation (which is a special kind of affine YM theory) in four dimensions is dimensionally reduced to the affine self-dual Chem-Simons equation in two dimensions. The latter is shown to have soliton solutions which satisfy the conformal affine Toda equations.
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.
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.
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.
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.
118740834
Composite-particle hydrodynamics from dyonic black branes
We construct effective hydrodynamics for composite particles in (2+1) dimensions carrying a magnetic flux by employing a holographic approach. The hydrodynamics is obtained by perturbation of the dyonic black brane solutions in the derivative expansion. We introduce a consistent way to avoid mixing of different orders in the expansion. Thanks to this method, it is possible to take the strong external magnetic field limit in the dual field theory. To compare our result with those for a composite particle system, we study several cases that correspond to special solutions of Einstein’s equation and Maxwell’s equations.
118419441
Multi-loop integrand reduction techniques
We review recent progress in D-dimensional integrand reduction algorithms for two loop amplitudes and give examples of their application to non-planar maximal cuts of the five-point all-plus helicity amplitude in QCD.
119294170
Topological charged black holes in generalized Hořava-Lifshitz gravity
As a candidate of quantum gravity in ultrahigh energy, the (3 + 1)-dimensional Horava-Lifshitz (HL) gravity with critical exponent z not equal 1 indicates anisotropy between time and space at short distance. In the paper, we investigate the most general z = d Horava-Lifshitz gravity in arbitrary spatial dimension d, with a generic dynamical Ricci flow parameter. and a detailed balance violation parameter epsilon. In arbitrary dimensional generalized HLd+1 gravity with z >= d at long distance, we study the topological neutral black hole solutions with general lambda in z = d HLd+1, as well as the topological charged black holes with lambda = 1 in z = d HLd+1. The HL gravity in the Lagrangian formulation is adopted, while in the Hamiltonian formulation, it reduces to Dirac-De Witt's canonical gravity with lambda = 1. In particular, the topological charged black holes in z = 5 HL6, z = 4 HL5, z = 3, 4 HL4, and z = 2 HL3 with lambda = 1 are solved. Their asymptotical behaviors near the infinite boundary and near the horizon are explored, respectively. We also study the behavior of the topological black holes in the (d + 1)-dimensional HL gravity with U(1) gauge field in the zero temperature limit and finite temperature limit, respectively. Thermodynamics of the topological charged black holes with lambda = 1, including temperature, entropy, heat capacity, and free energy are evaluated.
119300744
TeV scale universal seesaw, vacuum stability and heavy Higgs
A bstractWe discuss the issue of vacuum stability of standard model by embedding it within the TeV scale left-right universal seesaw model (called SLRM in the text). This model has only two coupling parameters (λ1, λ2) in the Higgs potential and only two physical neutral Higgs bosons (h, H). We explore the range of values for (λ1, λ2) for which the light Higgs boson mass Mh = 126 GeV and the vacuum is stable for all values of the Higgs fields. Combining with the further requirement that the scalar self couplings remain perturbative till typical GUT scales of order 1016 GeV, we find (i) an upper and lower limit on the second Higgs (H) mass to be within the range: 0.4 ≤ $ \frac{{{M_H}}}{{{v_R}}} $ ≤ 0.7, where the vR is the parity breaking scale and (ii) that the heavy vector-like top, bottom and τ partner fermions (P3, N3, E3) mass have an upper bound $ {M_{{{P_3},}}}_{{{N_3},{E_3}}}\leq {v_R} $. We discuss some phenomenological aspects of the model pertaining to LHC.
118592385
The complete KLT-map between gravity and gauge theories
A bstractWe present the complete map of any pair of super Yang-Mills theories to supergravity theories as dictated by the KLT relations in four dimensions. Symmetries and the full set of associated vanishing identities are derived. A graphical method is introduced which simplifies counting of states, and helps in identifying the relevant set of symmetries.