V. I. Tkach

Supersymmetric action for Bianchi type models

The superfield action for Bianchi type models is formulated on the basis of local n = 2 supersymmetry. It is shown that the supersymmetric action for these models has the form of the localized version of n = 2 supersymmetric quantum mechanics. This local symmetry procedure provides a well defined scheme for including matter.

FRW model and spontaneous breaking of supersymmetry

In this paper we consider the supersymmetric (SUSY) FRW models interacting with the simplest real scalar matter supermultiplet. For these models we obtain potentials, which allow spontaneous breaking of SUSY. This happens for k = 0 and k = 1 when the energy density of the vacuum of the scalar field is zero and also for k = 1 when this energy density is . This work is in memory of Dmitrij Vasilievich Volkov.

SPONTANEOUS BREAKING OF SUPERSYMMETRY IN COSMOLOGICAL MODELS AND SUPERGRAVITY THEORIES

In this work we have constructed the most general action for a set of complex homogeneous scalar supermultiplets interacting with the scale factor in the supersymmetric FRW model. It is shown that the local conformal time supersymmetry leads to a scalar field potential defined in terms of the Kahler potential and superpotential in the same combination as in supergravity (or effective superstring) theories. This scalar field potential depends on an arbitrary parameter α which is not fixed by conformal time supersymmetry and induces the spontaneous breaking of supersymmetry in supergravity theories.

Supersymmetric FRW model and the ground state of supergravity

In this work we construct the vacuum configuration of supergravity interacting with homogeneous complex scalar matter fields. The corresponding configuration is of the FRW model invariant under the n = 2 local conformal time supersymmetry, which is a subgroup of the four-dimensional spacetime supersymmetry. We show that the potential of the scalar matter fields is a function of the Kahler potential and of the arbitrary parameter . On the quantum level our model for the case is a specific supersymmetric quantum mechanics, which admits quantum states in supergravity, and the states with zero energy are described by the wave function of the FRW universe.

ON THE SCHRÖDINGER EQUATION WITH TIME AND ITS SQUARE ROOT REPRESENTATION IN THE SUPERSYMMETRIC QUANTUM MECHANICS

In the present work we obtain the N=2 superconformal version of quantum mechanics with time considered as dynamical on an equal footing with other variables. The resulting supersymmetric system of constraints realizes the square root representation of the Schrodinger equation with time.

ACTION FOR THE FRW MODEL AND COMPLEX MATTER FIELD WITH LOCAL SUPERSYMMETRY

On the basis of local n = 2 conformal supersymmetry we have constructed the supersymmetric action for a set of complex scalar supermultiplets in the FRW model. This action corresponds to dilaton - axion and chiral components of supergravity theory, and it is shown that the supersymmetric action of this model has the form of a local version of the supersymmetric quantum mechanics with spontaneous breaking of supersymmetry when the vacuum energy is zero.

EXTENDED SUPERSYMMETRY FOR THE BIANCHI-TYPE COSMOLOGICAL MODELS

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.

On the Schrödinger equation for the supersymmetric FRW model

Abstract We consider a time-dependent Schrodinger equation for the Friedmann–Robertson–Walker (FRW) model. We show that for this purpose it is possible to include an additional action invariant under reparametrization of time. The last one does not change the equations of motion for the minisuperspace model, but changes only the constraint. The same procedure is applied to the supersymmetric case.

n=4supersymmetry for the FRW model

In this work we have constructed the n=4 extended local conformal time supersymmetry for the Friedmann-Robertson-Walker (FRW) cosmological models. This is based on the superfield construction of the action, which is invariant under wordline local n=4 supersymmetry with

Dual symmetry and the vacuum energy

SU(2)_{local} \otimes SU(2)_{global}