`Conformal Theories - AdS Branes' Transform, or One More Face of AdS/CFT

The AdS/CFT transformation relates two nonlinear realizations of (super)conformal groups: their realization in the appropriate field theories in Minkowski space with a Goldstone dilaton field and their realization as (super)isometry groups of AdS (super)spaces. It exists already at the classical level and maps the field variables and space-time coordinates of the given (super)conformal field theory in $d$-dimensional Minkowski space ${\cal M}_d$ on the variables of a scalar codimension one (super)brane in AdS$_{d+1}$ in a static gauge, the dilaton being mapped on the transverse AdS brane coordinate. We explain the origin of this coordinate map and describe some its implications, in particular, in $d=1$ models of conformal and superconformal mechanics. We also give a suggestive geometric interpretation of this AdS/CFT transform in the pure bosonic case in the framework of an extended $2d+1$-dimensional conformal space involving extra coordinates associated with the generators of dilatations and conformal boosts.Comment: Latex, 16pp., Contribution to the proceedings of the Seminar ``Classical and Quantum Integrable Systems'' (Protvino, Russia, 8--11 Jan. 2003

Gauge Fields, Nonlinear Realizations, Supersymmetry

This is a brief survey of the all-years research activity in the Sector "Supersymmetry" (the former Markov Group) at the Bogoliubov Laboratory of Theoretical Physics. The focus is on the issues related to gauge fields, spontaneously broken symmetries in the nonlinear realizations approach, and diverse aspects of supersymmetry.Comment: 60 pages, a review paper, published in "Physics of Particles and Nuclei'; further typos correcte

N=4 supersymmetric Eguchi-Hanson sigma model in d=1

We show that it is possible to construct a supersymmetric mechanics with four supercharges possessing not conformally flat target space. A general idea of constructing such models is presented. A particular case with Eguchi--Hanson target space is investigated in details: we present the standard and quotient approaches to get the Eguchi--Hanson model, demonstrate their equivalence, give a full set of nonlinear constraints, study their properties and give an explicit expression for the target space metric.Comment: LaTeX, 9 page

Super K\"ahler oscillator from SU(2|1) superspace

We construct a new version of the worldline SU(2|1) superspace as a deformation of the standard N =4, d=1 superspace and show that it naturally provides off- and on-shell description of general supersymmetric K\"ahler oscillator model considered earlier at the classical level within the Hamiltonian approach. The basic object is a generalized chiral SU(2|1), d=1 superfield with the off-shell field content (2, 4, 2). The frequency of the oscillator and the strength of external magnetic field are defined by two parameters: the contraction parameter $m$ and the new parameter $\lambda$ which reflects the freedom in defining the chiral SU(2|1), d=1 superspace. We treat both classical and quantum cases.Comment: 0 + 13 pages, typos corrected, reference adde