24,845 research outputs found
`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 -dimensional Minkowski space
on the variables of a scalar codimension one (super)brane in AdS 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 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
-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
A New Superconformal Mechanics
In this paper we propose a new supersymmetric extension of conformal
mechanics. The Grassmannian variables that we introduce are the basis of the
forms and of the vector-fields built over the symplectic space of the original
system. Our supersymmetric Hamiltonian itself turns out to have a clear
geometrical meaning being the Lie-derivative of the Hamiltonian flow of
conformal mechanics. Using superfields we derive a constraint which gives the
exact solution of the supersymmetric system in a way analogous to the
constraint in configuration space which solved the original non-supersymmetric
model. Besides the supersymmetric extension of the original Hamiltonian, we
also provide the extension of the other conformal generators present in the
original system. These extensions have also a supersymmetric character being
the square of some Grassmannian charge. We build the whole superalgebra of
these charges and analyze their closure. The representation of the even part of
this superalgebra on the odd part turns out to be integer and not spinorial in
character.Comment: Superfield re-define
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
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