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...ual paradigm shift must eventually have serious implications for cosmology. Perhaps, the most radical modification of standard concepts required by the new theory is the holographic principle [1] [2] =-=[3]-=- [4]. The holographic principle requires that the degrees of freedom of a spatial region reside not in the interior as in an ordinary quantum field theory but on the surface of the region. Furthermore...

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...= 4). From the d = 3 analysis of this paper we will learn that some parameters of matter fields (masses) arise as moduli of certain auxiliary scalar fields. Recently, a remarkable conjecture was made =-=[17, 18, 19, 20, 21]-=- on the large N corre2spondence of a fundamental theory in AdS spaces to conformal theories on their boundaries. This conjecture is an important development of the physics of singletons [22, 23]. The...

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...lity” between 4d N = 4 supersymmetric U(N) Yang-Mills theory (realized on N D3 branes) and Type IIB string theory on AdS5 ×S5 [1,2,3,4,5]. The conjecture [2] has been further developed in for example =-=[6,7]-=-. Similar conjectures relate other conformal field theories to other string or supergravity backgrounds. These exciting conjectures offer both a possibility of providing a nonperturbative definition o...

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...2, 37, 38] and references therein. In particular, conformal Killing tensors arise explicitly in [32] and implicitly in [38] for similar reasons. Underlying this progress is the AdS/CFT correspondence =-=[20, 30, 40]-=-. Indeed, we shall use a version of this correspondence to prove Theorem 2 in §3 and to establish the algebraic structure of the symmetry algebra in §4. 2000 Mathematics Subject Classification. 70S10,...

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... have begun to play a central role in the “AdS/CFT correspondence” of quantum field theory. This is not the place for a complete survey of the relevant literature, but let me just refer the reader to =-=[2, 3, 11, 12, 13, 15, 25, 26, 27, 28, 31, 32, 40, 43, 50, 52]-=-. The principal geometric result of this paper is the following generalization of the perturbation result of [25]. The Lichnerowicz Laplacian (cf. [10]) is the operator ∆L defined on symmetric 2-tenso...

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...ature using the Noether method to determine the supersymmetric completion of the Einstein action. Recently these Chern-Simons terms have been of interest in connection with the AdS/CFT correspondence =-=[13,14,15]-=-. Indeed, following [15] we identify the background fields Φ of (2.7) with the “boundary values” of the AdS7 maximally extended supergravity multiplet and Γ[Φ] as the on-shell supergravity action (sui...

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... model and find a chiral symmetry phase transition of the first order. ∗ e-mail: horigome@krishna.th.phy.saitama-u.ac.jp † e-mail: tanii@phy.saitama-u.ac.jp1. Introduction The AdS/CFT correspondence =-=[1, 2, 3]-=- (see [4] for a review) is a useful duality between a string theory in (d + 1)-dimensional anti de Sitter spacetime (times a compact space) and a d-dimensional conformal field theory. The AdS/CFT corr...