International Journal of Modern Physics A

In this paper, we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang–Baxter and boundary Yang–Baxter equations depending on the choice of boundary conditions. The relation between the aforementioned equations and the braid group is briefly discussed. A short review on quantum groups as well as the quantum inverse scattering method (algebraic Bethe ansatz) is also presented.

A dynamical mechanism for symmetry breaking is investigated under the circumstances with the finite curvature, finite size and nontrivial topology. A four- and eight-fermion interaction model is considered as a prototype model which induces symmetry breaking at GUT era. Evaluating the effective potential in the leading order of the 1/N-expansion by using the dimensional regularization, we explicitly calculate the phase boundary which divides the symmetric and the broken phase in a weakly curved space–time and a flat space–time with nontrivial topology, R^D-1 ⊗ S¹.

We present a complete and minimal catalogue of MSSM gauge invariant monomials. That is, the catalogue of Gherghetta, Kolda and Martin is elaborated to include generational structure for all monomials. Any gauge invariant operator can be built as a linear combination of elements of the catalogue lifted to nonnegative integer powers. And the removal of any one of the monomials would deprive the catalogue of this feature. It contains 712 monomials, plus 3 generations of right-handed neutrinos if one extends the model to the νMSSM. We note that νMSSM flat directions can all be lifted by the sixth-order superpotential compared to the ninth-order needed in MSSM.

We show that the large N reduction holds on group manifolds. Large N field theories defined on group manifolds are equivalent to some corresponding matrix models. For instance, gauge theories on S³ can be regularized in a gauge invariant and SO(4) invariant manner.

By studying the previously known holographic supersymmetric renormalization group flow (Gowdigere–Warner) in four dimensions, we find the mass deformed Chern–Simons matter theory which has supersymmetry by adding the four mass terms among eight adjoint fields. The geometric superpotential from the 11 dimensions is found and provides the M2-brane probe analysis. As second example, we consider known holographic supersymmetric renormalization group flow (Pope–Warner) in four dimensions. The eight mass terms are added and similar geometric superpotential is obtained.

We consider a supersymmetric hybrid inflation in the framework of the Randall–Sundrum type II braneworld model. We derive an analytical expression for the scalar potential and find that the F-term dominates the hybrid inflation process. We show that, for some value of brane tension, we can eliminate the fine-tuning problem related to coupling constant κ of the potential. We also calculate all known spectrum inflation parameters and show that observational bounds from WMAP5, BAO and SN observations are satisfied.

The Dirac constraint formalism is used to analyze the first-order form of the Einstein–Hilbert action in d > 2 dimensions. Unlike previous treatments, this is done without eliminating fields at the outset by solving equations of motion that are independent of time derivatives when they correspond to first class constraints. As anticipated by the way in which the affine connection transforms under a diffeomorphism, not only primary and secondary but also tertiary first class constraints arise. These leave d(d-3) degrees of freedom in phase space. The gauge invariance of the action is discussed, with special attention being paid to the gauge generators of Henneaux, Teitelboim and Zanelli and of Castellani.

In this paper, we will present a general formalism for constructing the nonlinear charge coherent states which in special case lead to the standard charge coherent states. The su_Q(1, 1) algebra as a nonlinear deformed algebra realization of the introduced states is established. In addition, the corresponding even and odd nonlinear charge coherent states have also been introduced. The formalism has the potentiality to be applied to systems either with known "nonlinearity function" f(n) or solvable quantum system with known "discrete nondegenerate spectrum" e_n. As some physical appearances, a few known physical systems in the two mentioned categories have been considered. Finally, since the construction of nonclassical states is a central topic of quantum optics, nonclassical features and quantum statistical properties of the introduced states have been investigated by evaluating single- and two-mode squeezing, su(1, 1)-squeezing, Mandel parameter and antibunching effect (via g-correlation function) as well as some of their generalized forms we have introduced in the present paper.