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.
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.
14130582
Multiple reference states and complete spectrum of the Zn Belavin model with open boundaries
The multiple reference state structure of the Zn Belavin model with non-diagonal boundary terms is discovered. It is found that there exist n reference states, each of them yields a set of eigenvalues and Bethe Ansatz equations of the transfer matrix. These n sets of eigenvalues together constitute the complete spectrum of the model. In the quasi-classic limit, they give the complete spectrum of the corresponding Gaudin model.
119129139
Novel quasi-exactly solvable models with anharmonic singular potentials
We present new quasi-exactly solvable models with inverse quartic, sextic, octic and decatic power potentials, respectively. We solve these models exactly by means of the functional Bethe ansatz method. For each case, we give closed-form solutions for the energies and the wave functions as well as analytical expressions for the allowed potential parameters in terms of the roots of a set of algebraic equations.
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.
18230581
Supersymmetric extension of the sine-Gordon theory with integrable boundary interactions
Integrability and supersymmetry of the supersymmetric extension of the sine-Gordon theory on a half-line are examined and the boundary potential which preserves both the integrability and supersymmetry on the bulk is derived. It appears that unlike the boundary bosonic sine-Gordon theory, integrability and supersymmetry strongly restrict the form and parameters of the boundary potential, so that no free parameter in the boundary term is allowed up to a choice of signs.
67813587
Screening of cosmological constant in non-local cosmology
We consider a model of non-local gravity with a large bare cosmological constant, Λ, and study its cosmological solutions. The model is characterized by a function f(ψ) = f0eαψ, where ψ = □-1R and α is a real dimensionless parameter. In the absence of matter, we find an expanding universe solution a ∝ tn with n αcr ≈ 0.17. This is quite a weak condition. We argue that the solution is stable against the inclusion of matter fields. Thus our solution opens up new possibilities for solution to the cosmological constant problem.
118866595
Atmospheric Neutrino Mixing and b → s Transitions: Testing Lopsided SO(10) Flavor Structure in B physics
We point out that the correlation between the large atmospheric neutrino mixing and the b! s transition, if exists, comes from the lopsided flavor structure in SO(10) grand unification theory. We suggest testing the correlation by studying the deviation of SKS and S�'KS from the standard model predictions along with the constraints fromMBS and b! s in a realistic SO(10) model with lopsided flavor structure. We find a specific correlation between SKS and S�'KS that is intrinsic to the lopsided structure and discuss how to confirm or rule out this flavor pattern by the more accurate measurements of these CP violation quantities in B decay. The standard model (SM), although has passed many precision experimental tests, still has a number of out- standing problems which beg for a more fundamental the- ory. In terms of phenomenology, there are many places to test the more fundamental theory and, quite often, it is not one piece of phenomenology but a specific pattern of many pieces of phenomenology that fulfils this job. Neutrino oscillation clearly indicates the beyond SM physics in that it violates the accidental symmetry Le,µ,� of SM lepton flavor. Moreover, the tiny neutrino masses can be most naturally explained by the seesaw mech- anism (1), indicating the Majorana nature of neutrinos that leads to violation of another accidental symmetry B − L of SM at a very high scale close to the grand unification theory (GUT) scale. For this reason, study- ing neutrino oscillation in the GUT framework becomes particularly interesting. In SO(10) GUT, quarks and leptons are unified into a single 16 multiplet, yet experimental data shows that the 2-3 (generation) mixing is dramatically different in the quark and lepton sectors. While the quark mixing an- gle θ CKM is around 0.04, the lepton mixing angle θ PMNS (atmospheric mixing angle) is quite large and could be a maximum of π/4. This difference can be rather naturally explained by the lopsidedness in the 2-3 sector of mass matrices of down-type quarks and charged leptons:
41782509
Direct detection of baryogenesis mechanism from squark decays at LHC
We investigate the feasibility of directly detecting a generation mechanism of the cosmic baryon asymmetry by repeating the same particle physics process inside the LHC. We propose a framework with R-parity and CP violating squark decays responsible for baryogenesis, which can be embedded in supersymmetric models and is partly motivated by naturalness. We argue that the baryon number generation here is closely related to lepton charge asymmetry on the resonance. We emphasize the importance of the single charged lepton plus multijet channel in the absence of significant missing energy in search of such a scenario.
118465032
Integration-by-parts identities from the viewpoint of differential geometry
We present a new method to construct integration-by-part (IBP) identities from the viewpoint of differential geometry. Vectors for generating IBP identities are reformulated as differential forms, via Poincar\'{e} duality. Using the tools of differential geometry and commutative algebra, we can efficiently find differential forms which generate on-shell IBP relation without doubled propagator. Various $D=4$ two-loop examples are presented.
118460040
Cosmological solutions of a nonlocal model with a perfect fluid
A nonlocal gravity model which does not assume the existence of a new dimensional parameter in the action and includes a function f(−1R), with the d'Alembertian operator, is studied. By specifying an exponential form for the function f and including a matter sector with a constant equation of state parameter, all available power-law solutions in the Jordan frame are obtained. New power-law solutions in the Einstein frame are also probed. Furthermore, the relationship between power-law solutions in both frames, established through conformal transformation, is substantially clarified. The correspondence between power-law solutions in these two frames is proven to be a very useful tool in order to obtain new solutions in the Einstein frame.