We study the unitary supermultiplets of the N = 4 d = 7 anti-de Sitter (AdS 7 ) superalgebra OSp(8 * |4), with the even subalgebra SO(6, 2) × U Sp(4), which is the symmetry superalgebra of M-theory on AdS 7 × S 4 . We give a complete classification of the positive energy doubleton and massless supermultiplets of OSp(8 * |4). The ultra-short doubleton supermultiplets do not have a Poincaré limit in AdS 7 and correspond to superconformal field theories on the boundary of AdS 7 which can be identified with d = 6 Minkowski space. We show that the six dimensional Poincare mass operator m 2 = P µ P µ vanishes identically for the doubleton representations. By going from the compact U (4) basis of SO * (8) = SO(6, 2) to the noncompact basis SU * (4)×D (d = 6 Lorentz group times dilatations) one can associate the positive (conformal) energy representations of SO * (8) with conformal fields transforming covariantly under the Lorentz group in d = 6. The oscillator method used for the construction of the unitary supermultiplets of OSp(8 * |4) can be given a dynamical realization in terms of chiral super-twistor fields. CERN-TH/99-347 November, 1999 1 Work supported in part by the National Science Foundation under Grant Number PHY-9802510 2 e-mail: murat@phys.psu.edu 3 e-mail: takemae@phys.psu.edu. IntroductionRecently, a great deal of work has been done on AdS/CFT (anti-de Sitter/conformal field theory) dualities in various dimensions. The current interest in AdS/CFT dualities was sparked by the conjecture of Maldacena [1] relating the large N limits of certain conformal field theories in d dimensions to M-theory/string theory compactified to d+1-dimensional AdS spacetimes. Maldacena's conjecture was based on earlier work on properties of the physics of N Dp-branes in the near horizon limit [2] and the much earlier work on 10-d IIB supergravity compactified on AdS 5 × S 5 and 11-d supergravity compactified on AdS 7 × S 4 and AdS 4 × S 7 [3,4,5,6,7,8,9]. Maldacena's conjecture was formulated in a more precise manner in [10,11]. The relation between Maldacena's conjecture and the dynamics of the singleton and doubleton fields that live on the boundary of AdS spacetimes was reviewed in [12,13] and its relation to the spectra of maximal supergravities in eleven and ten dimensions in [13,14]. For a recent review of AdS/CFT dualities and an extensive list of references on the subject see [15].The best studied example of this AdS/CFT duality is the duality between the large N limit of the conformally invariant N = 4 SU (N ) super Yang-Mills theory in d = 4 and type IIB superstring theory on AdS 5 ×S 5 . The N = 4 Yang-Mills supermultiplet is simply the unique CPT self-conjugate doubleton supermultiplet of the symmetry superalgebra SU (2, 2|4) of type IIB superstring over AdS 5 × S 5 [4,16]. Doubleton supermultiplets do not have a smooth Poincaré limit in d = 5 and correspond to superconformal field theories on the boundary of AdS 5 , which can be identified with the four dimensional Minkowski space. The SU (2, 2|4) alg...

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In this paper, we describe a lab activity for measuring a spherical balloon's circumference. The procedure we discuss is based on the method used by Eratosthenes to measure the Earth's circumference.

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