Dynamic SU Research Articles

Describe of Nuclear Structure for Germanium (_32^66)Ge_34) Nucleus under frame (IBM-1, GVMI and VMI) Models

In this paper, the interacting bosons model-1 (IBM-1), a variable moment of inertia (VMI) and generalized moment of inertia (GVMI) models were used to calculate the energy levels of the positive parity and its gamma transitions as a function of the angular momentum of even-even (_32^66Ge_34) nucleus. To determine the dynamic symmetry of this nucleus, the ratios of the energy levels (E_4^+)⁄(E_2^+ ), (E_6^+)⁄(E_2^+), and (E_8^+)⁄(E_2^+) were evaluated and compared with experimental energy values and the ideal scheme of the three dynamic symmetries SU(5), SU(3), and O(6). The current study showed that the dynamic symmetry of this nucleus is determined to be O(6) - SU(5). The intersection of the energy band and the phenomenon of back bending were also studied using the (VMI) and (GVMI) models. These consequences were compared with the experimental results, and the results obtained have been in good agreement.

On supersymmetric AdS3 solutions of Type II

We classify supersymmetric warped AdS3×wM7 backgrounds of Type IIA and Type IIB supergravity with non-constant dilaton, generic RR fluxes and magnetic NSNS flux, in terms of a dynamic SU(3)-structure on M7. We illustrate our results by recovering several solutions with various amounts of supersymmetry. The dynamic SU(3)-structure includes a G2-structure as a limiting case, and we show that in Type IIB this is integrable.

Studying the nuclear structure of the () deformed nucleus by using (IBM-1) and (VAVM) Models

In this paper, the nuclear structure of the deformed even-even nucleus was studied using the first interacting boson model (IBM-1) to calculate the energy levels E(L) and the transitional energy (Eγ ). The energy bands, as well as the quadrupole moment (QL ) can be calculated to know the shape of the nucleus and the moment of inertia model, energy levels E(L), transitional energy (Eγ ) and the bands intersection. The current study showed that at dynamic symmetry SU (3), there is no effect of inertia moment on the shape of the rotational nuclei due to the absence of the phenomenon of back bending that belongs to this dynamic symmetry, through calculating the energy levels ratios found that nucleus belongs to the rotational dynamic symmetry SU (3). A comparison of the available practical results with the results calculated by (VAVM) and (IBM-1) showed that the (VAVM) model are better than the results calculated by (IBM-1).

Studying the Nuclear Structure of the () Deformed Nucleus using (IBM-1) and (GVMI) Models

In this research, some properties of the nuclear structure of even-even deformed nucleus were studied with dynamic symmetry SU (3). The energy levels E (L), excited energy levels (Eγ ), and electric quadrupole moment(QL ) were calculated using a set of parameters in the calculation to obtain a match with the practical values available using the first interacting boson model. IBM-1 and generalized variable moment of inertia (GVMI) model, The calculated results are in good agreement with the available practical values, especially, the values calculated according to the GVMI program. The phenomenon of band intersection, and back bending were also studied, the results showed no effect of the moment of inertia on the shape of the nucleus under consideration, because the back bending phenomenon was not occur.

Barut—Girardello Coherent States for Nonlinear Oscillator with Position-Dependent Mass

Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut—Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover, it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.

Order α′ heterotic domain walls with warped nearly Kähler geometry

We consider 1+3-dimensional domain wall solutions of heterotic supergravity on a six-dimensional warped nearly K\"ahler manifold $X_6$ in the presence of gravitational and gauge instantons of tanh-kink type as constructed in [arXiv:1109.3552]. We include first order $\alpha'$ corrections to the heterotic supergravity action, which imply a non-trivial Yang-Mills sector and Bianchi identity. We present a variety of solutions, depending on the choice of instantons, for the special case in which the SU(3) structure on $X_6$ satisfies $W_1^-=0$. The solutions preserve two real supercharges, which corresponds to $\mathcal{N}{=}1/2$ supersymmetry from the four-dimensional point of view. Besides serving as a useful framework for collecting existing solutions, the formulation in terms of dynamic SU(3) structures utilized here allows us to obtain new solutions in as yet unexplored corners of the instanton configuration space. Our approach thus offers a unified description of the embedding of tanh-kink-type instantons into half-BPS solutions of heterotic supergravity where the internal six-dimensional manifold has a warped nearly K\"ahler geometry

Non-Abelian T-duality, G 2-structure rotation and holographic duals of $ \mathcal{N} $ = 1 Chern-Simons theories

A new dynamic SU(3)-structure solution in type-IIA is found by T-dualising a deformation of the Maldacena-Nastase solution along an SU(2) isometry. It is argued that this is dual to a quiver gauge theory with multiple Chern-Simons levels. A clear way of defining Chern-Simons levels in terms of Page charges is presented, which is also used to define a Chern-Simons term for the G 2-structure analogue of Klebanov-Strassler, providing evidence of a cascade in both the ranks and levels of the dual quiver.

Supersymmetry of consistent massive truncations of type-IIB supergravity

We discuss the supersymmetry and fermionic sector of the recently obtained consistent truncations of IIB supergravity containing massive modes. In particular, we present the general form of the five-dimensional $\mathcal{N}=4$ supersymmetry transformations and equations of motion for the fermions arising in the reduction of IIB theory on ${T}^{1,1}$ which contains all modes invariant under the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ isometry group. The $\mathcal{N}=4$ reduction can be further truncated to two different $\mathcal{N}=2$ subsectors. For each of these, we present the $\mathcal{N}=2$ fermionic supersymmetry transformations and corresponding superpotentials. As an application, we obtain the explicit Killing spinors of the Klebanov-Strassler solution and comment on the relation to the ansatz of Papadopoulos and Tseytlin. We also demonstrate the applicability of consistent truncations on squashed Sasaki-Einstein manifolds to a class of flux compactifications, focusing on a recent solution describing the geometry of gaugino condensation on wrapped D7 branes and which possesses dynamic SU(2) structure.

Dynamic SU(2) structure from seven-branes

We obtain a family of supersymmetric solutions of type IIB supergravity with dynamic SU(2) structure, which describe the local geometry near a stack of four D7-branes and one O7-plane wrapping a rigid four-cycle. The deformation to a generalized complex geometry is interpreted as a consequence of nonperturbative effects in the seven-brane gauge theory. We formulate the problem for seven-branes wrapping the base of an appropriate del Pezzo cone, and in the near-stack limit in which the four-cycle is flat, we obtain an exact solution in closed form. Our solutions serve to characterize the local geometry of nonperturbatively-stabilized flux compactifications.

New supersymmetricAdS4type II vacua

Building on our recent results on dynamic SU(3)xSU(3) structures we present a set of sufficient conditions for supersymmetric AdS4xM6 backgrounds of type IIA/IIB supergravity. These conditions ensure that the background solves, besides the supersymmetry equations, all the equations of motion of type II supergravity. The conditions state that the internal manifold is locally a codimension-one foliation such that the five dimensional leaves admit a Sasaki-Einstein structure. In type IIA the supersymmetry is N=2, and the total six-dimensional internal space is locally an S^2 bundle over a four-dimensional Kaehler-Einstein base; in IIB the internal space is the direct product of a circle and a five-dimensional squashed Sasaki-Einstein manifold. Given any five-dimensional Sasaki-Einstein manifold we construct the corresponding families of type IIA/IIB vacua. The precise profiles of all the fields are determined at the solution and depend on whether one is in IIA or in IIB. In particular the background does not contain any sources, all fluxes (including the Romans mass in IIA) are generally non-zero, and the dilaton and warp factor are non-constant.

Crystal Ball physics

Selected results are presented for neutral final-state reactions produced by π − and K − beams incident on a proton target. Special attention is given to 2 π 0 production. Evidence is found for the applicability of dynamic SU(3) flavor symmetry. New data on η decays are included, such as two novel tests of C invariance. The experiments were carried out with the Crystal Ball multiphoton spectrometer in the C6 line of the AGS.

Dynamic SU(2) lattice gauge theory at finite temperature

The dynamic relaxation process for the (2+1)--dimensional SU(2) lattice gauge theory at critical temperature is investigated with Monte Carlo methods. The critical initial increase of the Polyakov loop is observed. The dynamic exponents $\theta$ and $z$ as well as the static critical exponent $\beta/\nu$ are determined from the power law behaviour of the Polyakov loop, the auto-correlation and the second moment at the early stage of the time evolution. The results are well consistent and universal short-time scaling behaviour of the dynamic system is confirmed. The values of the exponents show that the dynamic SU(2) lattice gauge theory is in the same dynamic universality class as the dynamic Ising model.

Coherent states and integrals over trajectories for the dynamic group SU(N)

This paper presents the explicit construction of integrals over trajectories for quantum systems possessing the dynamic group SU(N). N-level molecules are among such systems discussed. The dynamical group SU(N) describes the process of fermion pair generation with spin j in an external field, manifest in nuclear models with pairing. The integral over trajectories for a covariant symbol of the evolution operator is presented. The method developed in this paper can be used also on more complex systems that have the dynamic group SU(N), for instance, for the computation of nuclear models of the LipkinMeshov-Glick type extended to the case of the group SU(N).