The N = 2 Supersymmetric Unconstrained Matrix GNLS Hierarchies

The generalization of the N = 2 supersymmetric chiral matrix (k | n,m)-GNLS hierarchy (Lett. Math. Phys. 45 (1998) 63, solv-int/9711009) to the case when matrix entries are bosonic and fermionic unconstrained N = 2 superfields is proposed. This is done by exhibiting the corresponding matrix Lax-pair representation in terms of N = 2 unconstrained superfields. It is demonstrated that when matrix entries are chiral and antichiral N = 2 superfields, it reproduces the N = 2 chiral matrix (k | n,m)-GNLS hierarchy, while in the scalar case, k = 1, it is equivalent to the N = 2 supersymmetric multicomponent hierarchy (J. Phys. A 29 (1996) 1281, hep-th/9510185). The simplest example—the N = 2 unconstrained (1 | 1,0)-GNLS hierarchy—and its reduction to the N = 2 supersymmetric = 1 KdV hierarchy are discussed in more detail, and its rich symmetry structure is uncovered.     

N=4超对称量子力学

利用Clifford代数构造了N=4超对称量子力学的一般形式,并讨论了它的实现.     

A Note on the Third Family of N=2 Supersymmetric KdV Hierarchies

Abstract

We propose a hamiltonian formulation of the N = 2 supersymmetric KP type hierarchy recently studied by Krivonos and Sorin. We obtain a quadratic hamiltonian structure which allows for several reductions of the KP type hierarchy. In particular, the third family of N = 2 KdV hierarchies is recovered. We also give an easy construction of Wronskian solutions of the KP and KdV type equations.     

N=2 supersymmetric kinks and real algebraic curves

The kinks of the (1+1)-dimensional Wess-Zumino model with polynomic superpotential are investigated and shown to be related to real algebraic curves.     

N = 4 Supersymmetric (Dyonic) Hypermultiplets in String Theory

In four-dimensional N = 4 supersymmetric gauge theory, we obtain an exact metric on the moduli space of quantum vacua and analyze the spectra of BPS states in weak as well as in strong coupling regions. Identifying the hypermultiplet of the dyonic state as a string stretched between D₃-brane probe and a 7-brane, we demonstrate that the two hypermultiplets, which become massless at two singularities in supersymmetric theory, correspond to open strings beginning on the D₃-brane and ending on the respective 7-brane.     

The Hamiltonian structure of the N = 2 supersymmetric GNLS hierarchy

The first two Hamiltonian structures and the recursion operator connecting all evolution systems and Hamiltonian structures of the N = 2 supersymmetric (n, m)-GNLS hierarchy are constructed in terms of N = 2 superfields in two different superfield bases with local evolution equations. Their bosonic limits are studied in detail. New local and nonlocal bosonic and fermionic integrals both for the N = 2 supersymmetric (n, m)-GNLS hierarchy and its bosonic counterparts are derived. As an example, in the n = 1, m = 1 case, the algebra and the symmetry transformations for some of them are worked out and a rich N = 4 supersymmetry structure is uncovered.     

Soliton Solutions of the N=2 Supersymmetric KP Equation

Abstract

The N=2 super-KP equation associated with nonstandard flows is bilinearized using the Hirota method and soliton solutions are obtained. The bilinearization has been done for component fields and its KdV limit is discussed by comparing the soliton solutions obtained by this procedure with those found from the N=1 superspace formalism. The equivalence of these two procedures in the KdV limit is observed.     

N = 2 KP and KdV Hierarchies in Extended Superspace

We give the formulation in extended superspace of an N = 2 supersymmetric KP hierarchy using chirality preserving pseudo-differential operators. We obtain two quadratic hamiltonian structures, which lead to different reductions of the KP hierarchy. In particular we find two different hierarchies with the N = 2 classical super- algebra as a hamiltonian structure. The relation with the formulation in N=1 superspace and the bosonic limit are carried out. Received: 6 March 1997 / Accepted: 18 April 1997     

Superstring cosmology for N4 = 1 → 0 superstring vacua

We study the cosmology of perturbative heterotic superstring theory during the radiation‐like era for semi‐realistic backgrounds with initial 𝒩 = 1 supersymmetry. This analysis is valid for times after the Hagedorn era (or alternatively inflation era) but before the electroweak symmetry breaking transition. We find an attraction to a radiation‐like era with the ratio of the supersymmetry breaking scale to temperature stabilized. This provides a dynamical mechanism for setting the supersymmetry breaking scale and its corresponding hierarchy with the Planck scale. For the internal space, we find that orbifold directions never decompactify, while toroidal directions may decompactify only when they are wrapped by certain geometrical fluxes which break supersymmetry. This suggests a mechanism for generating spatial directions during the radiation‐like era. Moreover, we show that certain moduli may be stabilized during the radiation‐like era with masses near the supersymmetry breaking scale. In addition, the moduli do not dominate at late times, thus avoiding the cosmological moduli problem.     

N = 4 Supersymmetric Morse Oscillator and Its Spectrum-Generating Algebra

In this paper N = 4 supersymmetry of generalized Morse oscillators in one dimension is studied. Both bound states and scattering states of its four superpartner Hamiltonians are analyzed by using unitary irreducible representations of the noncompact Lie algebra su（1,1）. The spectrum-generating algebra governing the Hamiltonian of the N = 4 supersymmetric Morse oscillator is shown to be connected with the realization of Lie superalgebra osp（1,2） or B（0,1） in terms of the variables of a supersymmetric two-dimensional harmonic oscillator.     

N = 4 Supersymmetric Morse Oscillator and Its Spectrum-Generating Algebra

In this paper N = 4 supersymmetry of generalized Morse oscillators in one dimension is studied. Both bound states and scattering states of its four superpartner Hamiltonians are analyzed by using unitary irreducible representations of the noncompact Lie algebra su(1,1). The spectrum-generating algebra governing the Hamiltonian of the N = 4 supersymmetric Morse oscillator is shown to be connected with the realization of Lie superalgebra osp(1,2)or B(0,1) in terms of the variables of a supersymmetric two-dimensional harmonic oscillator.     

Supersymmetric Sawada-Kotera-Ramani Equation： Bilinear Approach

In this paper, using the Hirota＇s bilineax method, we consider the N = 1 supersymmetric Sawada-Kotera- Ramani equation and obtain the Bazcklund transformation of it. Its one- and two-supersoliton solutions axe obtained and N-supersoliton solutions for N ≥ 3 are given under the condition kiξj = kjξi.     

The gravity dual of the non-perturbativeN = 2 supersymmetric Yang-Mills theory

The anomalous Ward identity is derived forN = 2 SUSY Yang-Mills theories, which is resulted out of wrapping ofD ₅ branes on supersymmetric two cycles. Prom the ward identity one obtains the Witten-Dijkgraaf-Verlinde-Verlinde equation and hence can solve for the pre-potential. This way one avoids the problem of enhancon which maligns the non-perturbative behaviour of the Yang-Mills theory resulted out of wrapped branes.     

碱土金属氧化物阳离子2MO+(M=Ca,Sr,Ba)参与N2O与CO反应理论研究

本文采用UB3LYP/6-311G(2d) +SDD//CCSD(T)/6-311+ G(2d) +SDD方法,计算研究了气相中碱土金属氧化物阳离子2MO+ (M=Ca,Sr,Ba)参与N2O (X1∑+)+CO(X1∑+)→N2(X1∑g+)+CO2 (X1∑g+)的反应机理.通过计算亲氧性得到在三种氧化物阳离子中只有2CaO+从N2O得到O原子并传递给CO的过程是热力学允许的.碱土金属氧化物阳离子2MO+参与主题反应的机理通过以下两种方式进行,其一为2 MO+从N2O获取O原子生成2MO+,进而向CO提供O原子得到2MO+和CO2,该过程为催化反应机理;其二为2MO+先与N2O复合生成中间体IM1,之后IM1继续与CO复合生成中间体IM2',经过一系列反应过程最终生成2MO+,N2和CO2.通过对两种反应过程的热力学性质和动力学因素分析得到,2 MO+ (M=Ca,Sr,Ba)参与反应N2O(X1∑+)+CO(X1∑+)→N2(X1∑g+)+CO2(X1∑g+)的机理为后一路径,所得结果与实验观测相符.     

N=2超对称量子力学的新实现和形状不变性

构造新的超荷和定义权重函数,并研究了N=2一维超对称量子力学.在新的实现中讨论了若干实例.     

CoAlN(N=2-11)团簇基态结构的稳定性和磁性

采用密度泛函理论中的广义梯度近似(GGA),对CoAlN(N=2-11)团簇进行构型优化和磁性计算.在考虑自旋多重度的情况下得到了团簇的平衡构型及基态结构,并重点讨论了Co原子的sp-d杂化效应对体系稳定性和磁性的影响.结果表明:N为偶数时,团簇的基态为自旋双重态,Co原子磁矩随N增加整体上呈减小趋势;N为奇数时(除N=5为自旋三重态外),团簇的基态为自旋单重态,Co原子磁矩为零.N≥8时,Co原子陷入主团簇内部,体系的对称性降低,稳定性增强;轨道杂化增强了体系的稳定性,但减小了双重态和三重态体系中Co原子的磁矩;N=3,8,10是团簇CoAlN(N=2.11)的幻数.     

Theoretical Study on N = 126 Shell Evolution

The nuclei around magic number N = 126 are investigated in the deformed relativistic mean field (RMF) model with effective interactions TMA. We focus investigations on the N = 126 isotonic chain. The N = 126 shell evolution is studied by analyzing the variations of two-neutron (proton) separation energies, quadruple deformations, single particle levels etc. The good agreement of two-neutron separation energies between experimental data and calculated values is reached. The RMF theory predicts that the sizes of N = 126 shell become smaller and smaller with the increasing of proton number Z. However, the N = 126 shell exists in our calculated region all along. According to the calculated two-proton separation energies, the RMF theory suggests ²²⁰Pu is a two-proton drip-line nucleus in the N = 126 isotonic chain.