14543379
Partition function of the eight-vertex model with domain wall boundary condition
We derive the recursive relations of the partition function for the eight-vertex model on an N×N square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the explicit expression of the domain wall partition function of the model. In the trigonometric/rational limit, our results recover the corresponding ones for the six-vertex model.
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.
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.
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.
119077959
Probing natural SUSY from stop pair production at the LHC
A bstractWe consider the natural supersymmetry scenario in the framework of the R-parity conserving minimal supersymmetric standard model (called natural MSSM) and examine the observability of stop pair production at the LHC. We first scan the parameters of this scenario under various experimental constraints, including the SM-like Higgs boson mass, the indirect limits from precision electroweak data and B-decays. Then in the allowed parameter space we study the stop pair production at the LHC followed by the stop decay into a top quark plus a lightest neutralino or into a bottom quark plus a chargino. From detailed Monte Carlo simulations of the signals and backgrounds, we find the two decay modes are complementary to each other in probing the stop pair production, and the LHC with $ \sqrt{s}=14 $ TeV and 100 fb−1 luminosity is capable of discovering the stop predicted in natural MSSM up to 450 GeV. If no excess events were observed at the LHC, the 95% C.L. exclusion limits of the stop masses can reach around 537 GeV.
120297881
Thermodynamical fluctuations of meson fields for the Zimanyi-Moszkowski model
By using the real-time Green{close_quote}s function method with a pair cutoff approximation up to the second order, the thermodynamical fluctuation effects of meson fields on the Zimanyi-Moszkowski model are investigated. We find that in the fluctuation effects on the effective mass of the nucleon, the pressures are considerable in the low-baryon-density region and/or the high-temperature regions. The results of the Zimanyi-Moszkowski model and the Welecka model beyond the mean-field approximation are compared. {copyright} {ital 1997} {ital The American Physical Society}
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.
54060612
Petrov type I condition and Rindler fluid in vacuum Einstein-Gauss-Bonnet gravity
A bstractRecently the Petrov type I condition is introduced to reduce the degrees of freedom of the extrinsic curvature of a timelike hypersurface to the degrees of freedom in the dual Rindler fluid in Einstein gravity. In this paper we show that the Petrov type I condition holds for the solutions of vacuum Einstein-Gauss-Bonnet gravity up to the second order in the relativistic hydrodynamic expansion. On the other hand, if imposing the Petrov type I condition and Hamiltonian constraint on a finite cutoff hypersurface, the stress tensor of the relativistic Rindler fluid in vacuum Einstein-Gauss-Bonnet gravity can be recovered with correct first order and second order transport coefficients. The case in the non-relativistic hydrodynamic expansion is also discussed.
119221055
An integrand reconstruction method for three-loop amplitudes
A bstractWe consider the maximal cut of a three-loop four point function with massless kinematics. By applying Gröbner bases and primary decomposition we develop a method which extracts all ten propagator master integral coefficients for an arbitrary triple-box configuration via generalized unitarity cuts. As an example we present analytic results for the three loop triple-box contribution to gluon-gluon scattering in Yang-Mills with adjoint fermions and scalars in terms of three master integrals.