The even and odd supersymmetric Hunter-Saxton and Liouville equations

It is shown that two different supersymmetric extensions of the Harry Dym equation lead to two different negative hierarchies of the supersymmetric integrable equations. While the first one yields the known even supersymmetric Hunter-Saxton equation, the second one is a new odd supersymmetric Hunter-Saxton equation. It is further proved that these two supersymmetric extensions of the Hunter-Saxton equation are reciprocally transformed to two different supersymmetric extensions of the Liouville equation.     

The spectrum of a class of supersymmetric theories with false vacua

The spectrum of a supersymmetric quantum mechanics model, whose potential has a steep supersymmetric minimum and a broad non-supersymmetric minimum, is analyzed. With the exception of the supersymmetric ground state, the low-energy spectrum is found to be determined entirely by the non-supersymmetric well. The model is motivated by effective lagrangians proposed for supersymmetric QCD. It is speculated that in an equivalent field theory exhibiting a supersymmetric true vacuum and a non-supersymmetric false vacuum, the false vacuum can play an important rôle in the physics, and that the lowest energy excitations are extended field configurations involving a new mass scale.     

Supersymmetric Ising field theory

We construct the simplest solvable non-trivial (S ≠ 1) supersymmetric model: the supersymmetric Ising field theory. The supersymmetric generalization of the duality order/disorder algebra is discussed. Finally we attempt to “double” the model and comment on the connection between this doubled model and the unsolved problem of the supersymmetric sine-Gordon kink structure.     

Prospects for the measurement of B 0 s oscillations with the ATLAS detector at LHC

The feasibility for mass measurements of supersymmetric particles from minimal gauge mediated models in the ATLAS detector at the large hadron collider is studied using parameterized simulations. The covered models are characterized by having the supersymmetric tau as the only next-to-lightest supersymmetric particle (NLSP). Given independent measurements of the lightest Higgs mass and the NLSP lifetime, a sufficient number of supersymmetric particle mass measurements are performed such that all underlying model parameters are constrained.     

Supersymmetric structures of Dirac oscillators in commutative and noncommutative spaces

The supersymmetric properties of a charged planar Dirac oscillator coupling to a uniform perpendicular magnetic field are studied. We find that there is an N=2 supersymmetric structure in both commutative and noncommutative cases. We construct the generators of the supersymmetric algebras explicitly and show that the generators of the supersymmetric algebras can be mapped onto ones which only contain the left or right-handed chiral phonons by unitary transformations.     

Two new supersymmetric equations of Harry Dym type and their supersymmetric reciprocal transformations

A new N=1$N=1$ supersymmetric Harry Dym equation is constructed by applying supersymmetric reciprocal transformation to a trivial supersymmetric Harry Dym equation, and its recursion operator and Lax formulation are also obtained. Within the framework of symmetry approach, a class of 3rd order supersymmetric equations of Harry Dym type are considered. In addition to five known integrable equations, a new supersymmetric equation, admitting 5th order generalized symmetry, is shown to be linearizable through supersymmetric reciprocal transformation. Furthermore, its Lax representation and recursion operator are given so that the integrability of this new equation is confirmed.     

Perturbation theory and renormalization of supersymmetric Yang-Mills theories

We solve the problem of introducing, in supersymmetric Yang-Mills Lagrangians, a supersymmetric gauge breaking term and a Faddeev-Popov ghost interaction term. The resulting Lagrangian turns out to be invariant under a global symmetry transformation which is the supersymmetric extension of the Slavnov symmetry. We show that the complete analysis of all primitively divergent supergraphs ensures, in conjunction with the Slavnov identities, the renormalizability of the theory, once a supersymmetric and gauge invariant regularizing procedure has been introduced. We find that the simplest regularizing procedure is a generalization of the higher covariant derivatives method. In the case of interaction with matter fields we prove that no mass counter term is needed, in exact analogy with the model without gauge fields. Finally we show that, in the Abelian situation, a supersymmetric mass term for the vector multiplet can be introduced without spoiling the renormalizability, thus providing the supersymmetric extension of massive vector bosons theories.     

New avenues in supersymmetry and supergravity

We analyze the problem of constructing supersymmetric versions of gauge theories of particles and of gravity which have a closed supersymmetric algebra. Inparticular we present the basic no-go theorems that indicate that in four dimensions it is not possible to construct suitably extended supersymmetric versions of the above theories without drastic modification of the supersymmetric algebra. Two ways past the“N=3” barrier are discussed; that of central charges involved highly constrained versions which appearn difficult to quantize effectively, while the use of light-cone variables seems to be the most promising. We give light-cone gauge versions of supersymmetric Yang-Mills theories for all extended cases of interest and briefly consider their ultraviolet divergence properties.     

用超对称幺正变换解双光子过程的Jaynes-Cummings模型

本文发现了描写双光子过程的Jaynes-Cummings哈密顿量的超对称结构.根据超对称量子力学理论,引入了超对称幺正变换使其哈密顿量对角化.从而,得到了它的本征值、本征态,同时也计算了态的演化和跃迁几率.     

Do the quantum corrections to the soliton mass vanish?

The one-loop quantum corrections to the soliton mass are found to vanish for a large class of two-dimensional supersymmetric models and the three-dimensional supersymmetric CPⁿ model. This was achieved by quantizing in a box with supersymmetric boundary conditions.     

Reflection matrices for integrable N = 1 supersymmetric theories

We study two-dimensional integrable N = 1 supersymmetric theories (without topological charges) in the presence of a boundary. We find a universal ratio between the reflection amplitudes for particles that are related by supersymmetry and we propose exact reflection matrices for the supersymmetric extensions of the multi-component Yang-Lee models and for the breather multiplets of the supersymmetric sine-Gordon theory. We point out the connection between our reflection matrices and the classical boundary actions for the supersymmetric sine-Gordon theory as constructed by Inami, Odake and Zhang [Phys. Lett. B 359 (1995) 118].     

EXACT SOLUTION FOR SUPER-JAYNES-CUMMINGS MODEL

Based on the linear quantum transformation theory, we further propose a supersymmetric unitary transformation, whose operator can be constructed by the supersymmetric generators of Lie superalgebra. Therefore, by making use of the supersymmetric unitary transformation, we can obtain the eigenspectrum, the eigenstates and the super-partition function for the Super-Jaynes-Cummings model when the coupling constants are Grrassmann valued.     

Infra-red stable fixed points of Yukawa couplings in supersymmetric models

We provide the solutions of the fixed point conditions of the Yukawa sector for a large class of N = 1 supersymmetric theories including the minimal and next-to-minimal supersymmetric standard models and their grand unified and other extensions. We also introduce a test which can discriminate between infra-red stable, infra-red unstable and saddle point solutions, and illustrate our methods with the example of the next-to-minimal supersymmetric standard model. We show that in this case, the fixed point prediction of the top quark mass is equivalent to that of the minimal supersymmetric standard model, supporting previous numerical analyses.     

Supersymmetric quantum hall liquid with a deformed supersymmetry

We construct a supersymmetric quantum Hall liquid with a deformed supersymmetry. One parameter is introduced in the supersymmetric Laughlin wavefunction to realize the original Laughlin wavefunction and the Moore—Read wavefunction in two extremal limits of the parameter. The introduced parameter corresponds to the coherence factor in the BCS theory. It is pointed out that the parameter-dependent supersymmetric Laughlin wavefunction enjoys a deformed supersymmetry. Based on the deformed supersymmetry, we construct a pseudopotential Hamiltonian whose groundstate is exactly the parameter-dependent supersymmetric Laughlin wavefunction. Though the SUSY pseudopotential Hamiltonian is parameter-dependent and non-Hermitian, its eigenvalues are parameter-independent and real.     

Superfield approach to the construction of effective action in quantum field theory with extended supersymmetry

We review the current state of research on the construction of effective actions in supersymmetric quantum field theory. Special attention is paid to gauge models with extended supersymmetry in the superfield approach. The advantages of formulation of such models in harmonic superspace for the calculation of effective action are emphasized. Manifestly supersymmetric and manifestly gauge-invariant methods for constructing the low-energy effective actions and deriving the corrections to them are considered and the possibilities to obtain the exact solutions are discussed. The calculations of one-loop effective actions in N = 2 supersymmetric Yang–Mills theory with hypermultiplets and in N = 4 supersymmetric Yang–Mills theory are analyzed in detail. The relationship between the effective action in supersymmetric quantum field theory and the low-energy limit in superstring theory is discussed.     

Spin analysis of supersymmetric particles

The spin of supersymmetric particles can be determined at e⁺e^- colliders unambiguously. This is demonstrated for a characteristic set of non-colored supersymmetric particles – smuons, selectrons, and charginos/neutralinos. The analysis is based on the threshold behavior of the excitation curves for pair production in e⁺e^- collisions, the angular distribution in the production process and decay angular distributions. In the first step we present the observables in the helicity formalism for the supersymmetric particles. Subsequently we confront the results with corresponding analyses of Kaluza–Klein particles in theories of universal extra space dimensions which behave distinctly different from supersymmetric theories. It is shown in the third step that a set of observables can be designed which signal the spin of supersymmetric particles unambiguously without any model assumptions. Finally in the fourth step it is demonstrated that the determination of the spin of supersymmetric particles can be performed experimentally in practice at an e⁺e^- collider.     

The q-Deformation of the Superoscillators and Their q-Supercoherent States

We discuss the superoscillators in thc supersymmetric quantum systems, and give the solution to the system. By making use of the annihilation and creation operators and their q-deformed operators, we also give the q-deformed quantum harmonic oscillator model in the supersymmetric quantum systems. The q-supercoherent states associated with the q-deformed supersymmetric quantum harmonic oscillators are constructed explicitly, and their properties are investigated. The uncertainty relations for q-supercoherent states are discussed as well.     

Supersymmetric Pair Coherent States

Based on the permu table property between the two-mode boson-fermion annihilator for a supersymmetric harmonic oscillator, which is described by H = b^↑b + f^↑f, and the "charge" operators b^↑b - f^↑f we construct the supersymmetric pair coherent state. The super-lie algebra associated with the supersymmetric pair coherent state is analyzed.     

Invariant theory and exact solutions of the time-dependent supersymmetric two-level multiphoton Jaynes－Cummings model

On the basis of the fact that the two-level multiphoton Jaynes－Cummings (TLMJC) model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (the time-independent invariant). In this paper, we investigate the invariant-related unitary transformation approach to exact solutions of the time-dependent TLMJC model.     

A supersymmetric black ring

A new supersymmetric black hole solution of five-dimensional supergravity is presented. It has an event horizon of topology S1 x S2. This is the first example of a supersymmetric, asymptotically flat black hole of nonspherical topology. The solution is uniquely specified by its electric charge and two independent angular momenta. These conserved charges can be arbitrarily close, but not exactly equal, to those of a supersymmetric black hole of spherical topology.