120019613
Cohomology in connection space, family index theorem, and Abelian gauge structure
Using the natural connection form on a principal bundle P(M,G) and the bundle A (A /G,G) a systematic derivation of the double‐cohomological series constituted by the exterior differential d on space‐time M and arbitrary, horizontal, and vertical variations in connection space is given. The relationship between these cohomologies and the family index theorem is clarified. The formalism is then used to analyze Abelian gauge structure inside non‐Abelian gauge theory. The pertinent functional U(1) connection form, curvature form, and three‐form ‘‘curvature’’ are identified and computed, and are related to the θ vacuum, anomalous commutation relation, and Jacobi identity, respectively. Some of the results differ from those obtained by Wu and Zee [Nucl. Phys. B 258, 157 (1985)] and Niemi and Semenoff [Phys. Rev. Lett. 55, 227 (1985)] and the results of this paperrecover theirs under certain conditions. Finally the generalization of the formalism to a nontrivial principal bundle by introduction of a fixed backg...
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.
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.
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.
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.
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.
121435769
Phase Structure of Strange Matter in a Non-topological Soliton Model
A non-topological soliton model with strange quarks is suggested to investigate the phase structure of strange matter. The results are qualitatively in agreement with that obtained by MIT bag model provided the ratio of coupling constants of different quarks to soliton scalar field chi(sigma) = g(s sigma)/g(q sigma) larger than a critical value chi(c) similar to 0.86, but as chi(sigma) gets smaller than chi(c), the phase structure may change.
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.
119120163
Current experimental bounds on stop mass in natural SUSY
A bstractMotivated by the recent progress of direct search for the productions of stop pair and sbottom pair at the LHC, we examine the constraints of the search results on the stop ($ \widetilde{t} $1) mass in natural SUSY. We first scan the parameter space of natural SUSY in the framework of MSSM, considering the constraints from the Higgs mass, B-physics and electroweak precision measurements. Then in the allowed parameter space we perform a Monte Carlo simulation for stop pair production followed by $ \widetilde{t} $1 → t$ \widetilde{\chi}_1^0 $ or $ \widetilde{t} $1 → b$ \widetilde{\chi}_1^{+} $ and sbottom pair production followed by $ \widetilde{b} $1 → b$ \widetilde{\chi}_1^0 $ or $ \widetilde{b} $1 → t$ \widetilde{\chi}\overline{1} $. Using the combined results of ATLAS with 20.1 fb−1 from the search of ℓ + jets + T , hadronic $ t\overline{t} $ + T and 2b + T , we find that a stop lighter than 600 GeV can be excluded at 95% CL in this scenario.
30742433
Yukawa bound states of a large number of fermions
A bstractWe consider the bound state problem for a field theory that contains a Dirac fermion χ that Yukawa couples to a (light) scalar field ϕ. We are interested in bound states with a large number N of χ particles. A Fermi gas model is used to numerically determine the dependence of the radius R of these bound states on N and also the dependence of the binding energy on N. Since scalar interactions with relativistic χ’s are suppressed two regimes emerge. For modest values of N the state is composed of non-relativistic χ particles. In this regime as N increases R decreases. Eventually the core region becomes relativistic and the size of the state starts to increase as N increases. As a result, for fixed Yukawa coupling and χ mass, there is a minimum sized state that occurs roughly at the value of N where the core region first becomes relativistic. We also compute an elastic scattering form factor that can be relevant for direct detection if the dark matter is composed of such χ particles.
16162566
Possible implications of the channeling effect in NaI(Tl) crystals
The channeling effect of low energy ions along the crystallographic axes and planes of NaI(Tl) crystals is discussed in the framework of corollary investigations on WIMP dark matter candidates. In fact, the modeling of this existing effect implies a more complex evaluation of the luminosity yield for low energy recoiling Na and I ions. In the present paper related phenomenological arguments are developed and possible implications are discussed at some extent.