Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-12-07
Mod.Phys.Lett. A14 (1999) 147-160
Physics
High Energy Physics
High Energy Physics - Theory
Eq.(38) besides some typos are corrected. Latex file, 16 pages
Scientific paper
10.1142/S0217732399000183
As a toy model to search for Hamiltonian formalism of the $AdS/CFT$ correspondence, we examine a Hamiltonian formulation of the $AdS_2/CFT_1$ correspondence emphasizing unitary representation theory of the symmetry. In the course of a canonical quantization of the bulk scalars, a particular isomorphism between the unitary irreducible representations in the bulk and boundary theories is found. This isomorphism defines the correspondence of field operators. It states that field operators of the bulk theory are field operators of the boundary theory by taking their boundary values in a due way. The Euclidean continuation provides an operator formulation on the hyperbolic coordinates system. The associated Fock vacuum of the bulk theory is located at the boundary, thereby identified with the boundary CFT vacuum. The correspondence is interpreted as a simple mapping of the field operators acting on this unique vacuum. Generalization to higher dimensions is speculated.
Nakatsu Toshio
Yokoi Naoto
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