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The dynamical (super)symmetries for various monopole systems are reviewed. For a Dirac monopole, non-smooth Runge–Lenz vector can exist; there is, however, a spectrum-generating conformal o(2,1) dynamical symmetry that extends into osp(1/1) or osp(1/2) for spin 1/2 particles. Self-dual 't Hooft–Polyakov-type monopoles admit an su(2/2) dynamical supersymmetry algebra, which allows us to reduce the fluctuation equation to the spin 0 case. For large r, the system reduces to a Dirac monopole plus a suitable inverse-square potential considered before by McIntosh and Cisneros, and by Zwanziger in the spin 0 case, and to the "dyon" of D'Hoker and Vinet for spin 1/2. The asymptotic system admits a Kepler-type dynamical symmetry as well as a "helicity-supersymmetry" analogous to the one Biedenharn found in the relativistic Kepler problem. Similar results hold for the Kaluza–Klein monopole of Gross–Perry–Sorkin. For the magnetic vortex, the N = 2 supersymmetry of the Pauli Hamiltonian in a static magnetic field in the plane combines with the o(2) × o(2,1) bosonic symmetry into an o(2) × osp(1/2) dynamical superalgebra.

We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In the first part, we review in detail how higher Chern–Simons theories arise in the AKSZ-formalism. These theories form a universal starting point for the construction of $L_{\infty }$-algebra models. We then show how to describe superconformal field theories and how to perform dimensional reductions in this context. In the second part, we demonstrate that Nambu–Poisson and multisymplectic manifolds are closely related via their Heisenberg algebras. As a byproduct of our discussion, we find central Lie $p$-algebra extensions of $𝔰𝔬(p+2)$. Finally, we study a number of $L_{\infty }$-algebra models which are physically interesting and which exhibit quantized multisymplectic manifolds as vacuum solutions.

We present a definition of a (super)-modular functor which includes certain interesting cases that previous definitions do not allow. We also introduce a notion of topological twisting of a modular functor, and construct formally a realization by a 2-dimensional topological field theory valued in twisted $K$-modules. We discuss, among other things, the $N=1$-supersymmetric minimal models from the point of view of this formalism.

We study the bilinearization of $N=1$ Supersymmetric Coupled Dispersionless (SUSY-CD) integrable system by introducing transformations defined in terms of bosonic and fermionic superfields. From the bosonic and fermionic superfield bilinear equations, we obtain the superfield soliton solutions of SUSY-CD integrable system.

We construct the manifestly Lorenz-invariant formulation of the N = 1, D=4 massive superparticle with tensorial central charges. The model contains a real parameter k and at k≠0 possesses one κ-symmetry while at k=0 the number of κ-symmetry is two. The equivalence of the formulations at all k≠0 is obtained. The local transformations of κ-symmetry are written. It is considered using the index spinor for construction of the tensorial central charges. The equivalence at classical level between the massive D=4 superparticle with one κ-symmetry and the massive D=4 spinning particle is obtained.

The program to construct minimum-uncertainty coherent states for general potentials works transparently with solvable analytic potentials. However, when an analytic potential is not completely solvable, like for a double-well or the linear (gravitational) potential, there can be a conundrum. Motivated by supersymmetry concepts in higher dimensions, we show how these conundrums can be overcome.

We consider the noncommutative hypermultiplet model within harmonic superspace approach. The one-loop four-point contributions to the effective action of self-interacting q-hypermultiplet are computed. This model has two coupling constants instead of a single one in commutative case. It is shown that both coupling constants are generated by one-loop quantum corrections in the model of q-hypermultiplet interacting with vector multiplet. The holomorphic effective action of q-hypermultiplet in external gauge superfield is calculated. For the fundamental representation there is no uv/ir-mixing and the holomorphic potential is a ⋆-product generalization of a standard commutative one. For the adjoint representation of U(N) gauge group the leading contributions to the holomorphic effective action are given by the terms respecting for the uv/ir-mixing which are related to U(1) phase of U(N) group.

We investigate a quantum system possessing a parasupersymmetry of order 2, an orthosupersymmetry of order p, a fractional supersymmetry of order p+1, and topological symmetries of type (1,p) and (1,1,…,1). We obtain the corresponding symmetry generators, explore their relationship, and show that they may be expressed in terms of the creation and annihilation operators for an ordinary boson and orthofermions of order p. We give a realization of parafermions of order 2 using orthofermions of arbitrary order p, discuss a p=2 parasupersymmetry between p = 2 parafermions and parabosons of arbitrary order, and show that every orthosupersymmetric system possesses topological symmetries. We also reveal a correspondence between the orthosupersymmetry of order p and the fractional supersymmetry of order p+1.

In this work, we address the phenomenological consequences of explicit CP violation on direct Higgs–boson searches at high energy colliders. Having a restricted parameter space, we concentrate on the recently proposed gluino–axion model, and investigate the CP violation capability of the model subject to the recent experimental data. It is shown that the Higgs masses as well as their CP compositions are quite sensitive to the supersymmetric CP phases. The lightest Higgs is found to be nearly CP even to a good approximation whilst the remaining two heavy scalars do not have definite CP parities.

The n-instanton contribution to the Seiberg–Witten prepotential of N = 2 supersymmetric d = 4 Yang–Mills theory is represented as the integral of the exponential of an equivariantly exact form. Integrating out an overall scale and a U(1) angle the integral is rewritten as (4n - 3)-fold product of a closed two-form. This two-form is, formally, a representative of the Euler class of the instanton moduli space viewed as a principal U(1) bundle, because its pullback under bundle projection is the exterior derivative of an angular one-form.

The dynamical breaking of the supergauge symmetry in the massless supergauge Wess–Zumino model is discussed without adding the Fayet–Iliopoulos term to the Lagrangian. It is shown, in terms of the Nambu–Jona-Lasinio mechanism, that the supergauge symmetry breaking can be realized dynamically in the massless supergauge Wess–Zumino model. The supergauge symmetry behavior at finite temperatures is also investigated and it is shown that the supergauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.

Applying standard mathematical methods, it is explicitly shown how the Riccati equation for the Hubble parameter H (η) of barotropic open FRW cosmologies is connected with a Korteweg-de Vries equation for adiabatic index solitons. It is also shown how one can embed a discrete sequence of adiabatic indices of the type , (γ ≠ 2/3), in the sech FRW adiabatic index soliton.

Order-p parasupersymmetric and orthosupersymmetric quantum mechanics are shown to be fully reducible when they are realized in terms of the generators of a generalized deformed oscillator algebra and a ℤ_p+1-grading structure is imposed on the Fock space. The irreducible components provide p + 1 sets of bosonized operators corresponding to both unbroken and broken cases. Such a bosonization is minimal.

In the previous paper we studied Dirac fermions in a non-Abelian random vector potential by using lattice supersymmetry. By the lattice regularization, the system of disordered Dirac fermions is defined without any ambiguities. We showed that at strong-disorder limit correlation function of the fermion local density of states decays algebraically at the band center. In this paper, we shall re-examine the multi-flavor or multi-species case rather in detail and argue that the correlator at the band center decays exponentially for the case of a large number of flavors. This means that a delocalization–localization phase transition occurs as the number of flavors is increased. This discussion is supported by the recent numerical studies on multi-flavor QCD at the strong-coupling limit, which shows that the phase structure of QCD drastically changes depending on the number of flavors. The above behavior of the correlator of the random Dirac fermions is closely related with how the chiral symmetry is realized in QCD.

Six-dimensional compactification of type IIA matrix model on the Z-orbifold is studied. Introducing a Z₃ symmetry properly on the three mirror images of fields in the N-body system of the supersymmetric D0 particles, the action of the matrix model compactified on the Z-orbifold is obtained. In this matrix model supersymmetry is explicitly demonstrated.

We find nonsupersymmetric and supersymmetric solutions of D3 brane configuration in the background of pp-wave obtained as a Penrose limit of AdS₅ × S⁵.

We outline a general method for obtaining exact solutions of Schrödinger equations with a position-dependent effective mass and compare the results with those obtained within the frame of supersymmetric quantum theory. We observe that the distinct effective mass Hamiltonians proposed in the literature in fact describe exactly equivalent systems having identical spectra and wave functions as far as exact solvability is concerned. This observation clarifies the Hamiltonian dependence of the band-offset ratio for quantum wells.

We discuss the relationship between exact solvability of the Schrödinger equation with a position-dependent mass and the ordering ambiguity in the Hamiltonian operator within the framework of supersymmetric quantum mechanics. The one-dimensional Schrödinger equation, derived from the general form of the effective mass Hamiltonian, is solved exactly for a system with exponentially changing mass in the presence of a potential with similar behaviour, and the corresponding supersymmetric partner Hamiltonians are related to the effective-mass Hamiltonians proposed in the literature.

In this paper we propose a superfield description for all Bianchi-type cosmological models. The action is invariant under world-line local n = 4 supersymmetry with SU(2)_local ⊗ SU(2)_global internal symmetry. Due to the invariance of the action we obtain the constraints, which form a closed superalgebra of the n = 4 supersymmetric quantum mechanics. This procedure provides the inclusion of supermatter in a systematic way.

We discuss the decoupling solution to SUSY flavor problem in the fat brane scenario. We present a simple model to yield the decoupling sfermion spectrum in a five-dimensional theory. Sfermion masses are generated by the overlap between the wave functions of the matter fields and the chiral superfields on the SUSY breaking brane. Two explicit examples of the spectrum are given.