Geodesic
Conformal Theories--A{d}S Branes Transform, or One More Face of A{d}S/CFT
Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 1, pp. 77-95

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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 already exists 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 ${\mathcal M}_d$ to the variables of a scalar codimension-one (super)brane in $AdS_{d+1}$ in a static gauge, the dilaton being mapped onto the transverse AdS brane coordinate. We explain the origin of this coordinate mapping 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 transformation in the purely 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.
Keywords: supersymmetry, branes, nonlinear realizations, AdS space. 
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     author = {E. A. Ivanov},
     title = {Conformal {Theories--A{d}S} {Branes} {Transform,} or {One} {More} {Face} of {A{d}S/CFT}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {77--95},
     publisher = {mathdoc},
     volume = {139},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_139_1_a5/}
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E. A. Ivanov. Conformal Theories--A{d}S Branes Transform, or One More Face of A{d}S/CFT. Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 1, pp. 77-95. http://geodesic.mathdoc.fr/item/TMF_2004_139_1_a5/