Comments On Hamiltonian Formalism Of $AdS/CFT$ correspondence

Details Comments On Hamiltonian Formalism Of $AdS/CFT$ correspondence Comments On Hamiltonian Formalism Of $AdS/CFT$ correspondence

1998-12-07

arxiv.org/abs/hep-th/9812047v2

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.

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