N=4 Supersymmetry and the BPST Instanton

In this paper we construct the Lagrangian and Hamiltonian formulations of N=4 supersymmetric systems describing the motion of an isospin particle on a conformally flat four-manifold with SO(4) isometry carrying the non-Abelian field of a BPST instanton. The conformal factor can be specified to yield various particular systems, such as superconformally invariant mechanics as well as a particle on the four-sphere, the pseudosphere or on R x S^3. The isospin degrees of freedom arise as bosonic components of an additional fermionic N=4 supermultiplet, whose other components are rendered auxiliary by a nonlocal redefinition. Our on-shell component action coincides with the one recently proposed in arXiv:0912.3289.Comment: 1+8 pages; v2: two references added, published versio

Phase transitions and gaps in quantum random energy models

By using a previously established exact characterization of the ground state of random potential systems in the thermodynamic limit, we determine the ground and first excited energy levels of quantum random energy models, discrete and continuous. We rigorously establish the existence of a universal first order quantum phase transition, obeyed by both the ground and the first excited states. The presence of an exponentially vanishing minimal gap at the transition is general but, quite interestingly, the gap averaged over the realizations of the random potential is finite. This fact leaves still open the chance for some effective quantum annealing algorithm, not necessarily based on a quantum adiabatic scheme.Comment: 8 pages, 4 figure

Superfield Formulation of Nonlinear N=4 Supermultiplets

We propose a unified superfield formulation of N=4 off-shell supermultiplets in one spacetime dimension using the standard N=4 superspace. The main idea of our approach is a "gluing" together of two linear supermultiplets along their fermions. The functions defining such a gluing obey a system of equations. Each solution of this system provides a new supermultiplet, linear or nonlinear, modulo equivalence transformations. In such a way we reproduce all known linear and nonlinear N=4, d=1 supermultiplets and propose some new ones. Particularly interesting is an explicit construction of nonlinear N=4 hypermultiplets.Comment: 16 pages, no figure

Extended supersymmetric multiparticle Euler-Calogero-Moser model

We review the construction of supersymmetric extension of the n-particle Euler-Calogero-Moser model within the Hamiltonian approach [1]. The main feature of the proposed supersymmetrization method is that it is automatically adapted for a model with an arbitrary even number of supersymmetries. It is shown that the number of fermions that must be used in this construction is 1/2N n(n+1). We demonstrate that the resulting supersymmetric system is dynamically invariant with respect to the superconformal group and give the explicit realization of its generators in terms of the conserved currents. For the simplest case of the supersymmetric n-particle Euler-Calogero-Moser model we provide its description in superspace by using the corresponding constrained superfields. © 2019 Published under licence by IOP Publishing Ltd

BRST charges for finite nonlinear algebras

Some ingredients of the BRST construction for quantum Lie algebras are applied to a wider class of quadratic algebras of constraints. We build the BRST charge for a quantum Lie algebra with three generators and ghost-anti-ghosts commuting with constraints. We consider a one-parametric family of quadratic algebras with three generators and show that the BRST charge acquires the conventional form after a redefinition of ghosts. The modified ghosts form a quadratic algebra. The family possesses a non-linear involution, which implies the existence of two independent BRST charges for each algebra in the family. These BRST charges anticommute and form a double BRST complex.Comment: 10 page

Dynamical supersymmetry of spin particle-magnetic field interaction

We study the super and dynamical symmetries of a fermion in a monopole background. The Hamiltonian also involves an additional spin-orbit coupling term, which is parameterized by the gyromagnetic ratio. We construct the superinvariants associated with the system using a SUSY extension of a previously proposed algorithm, based on Grassmann-valued Killing tensors. Conserved quantities arise for certain definite values of the gyromagnetic factor: $\N=1$ SUSY requires $g=2$; a Kepler-type dynamical symmetry only arises, however, for the anomalous values $g=0$ and $g=4$. The two anomalous systems can be unified into an $\N=2$ SUSY system built by doubling the number of Grassmann variables. The planar system also exhibits an $\N=2$ supersymmetry without Grassmann variable doubling.Comment: 23 page

New Super Calogero Models and OSp(4|2) Superconformal Mechanics

We report on the new approach to constructing superconformal extensions of the Calogero-type systems with an arbitrary number of involved particles. It is based upon the superfield gauging of non-abelian isometries of some supersymmetric matrix models. Among its applications, we focus on the new N=4 superconformal system yielding the U(2) spin Calogero model in the bosonic sector, and the one-particle case of this system, which is a new OSp(4|2) superconformal mechanics with non-dynamical U(2) spin variables. The characteristic feature of these models is that the strength of the conformal inverse-square potential is quantized.Comment: 12 pages, talk presented by E.Ivanov at the XIII International Conference "Symmetry Methods in Physics", Dubna, July 6-9, 200

New Spinor Field Realizations of the Non-Critical W3W_{3} String

We investigate the new spinor field realizations of the $W_{3}$ algebra, making use of the fact that the $W_{3}$ algebra can be linearized by the addition of a spin-1 current. We then use these new realizations to build the nilpotent Becchi-Rouet-Stora--Tyutin (BRST) charges of the spinor non-critical $W_{3}$ string.Comment: 8 pages, no figures, revtex4 style, accepted by Chin. Phys. Let