Comments On Hamiltonian Formalism Of $AdS/CFT$ correspondence

Abstract

As a toy model to search for Hamiltonian formalism of the $AdS/CFT$ correspondence, we examine a Hamiltonian formulation of the $Ad{S}_2/CF{T}_1$ 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.

Eq.(38) besides some typos are corrected. Latex file, 16 pages

References in corpus (6)

• Gauge Theory Correlators from Non-Critical String Theory
• AdS Dynamics from Conformal Field Theory
• AdS2 Quantum Gravity and String Theory
• Black Holes and Superconformal Mechanics
• Spectrum of Large N Gauge Theory from Supergravity
• Gauge fields as composite boundary excitations

Cited by in corpus (15)

• The Extreme Kerr Throat Geometry: A Vacuum Analog of AdS_2 x S^2
• Conformal quantum mechanics as the CFT${}_1$ dual to AdS${}_2$
• Schwinger pair production in AdS2
• w_{\infty} Algebras, Conformal Mechanics, and Black Holes
• Mass Spectrum of D=11 Supergravity on AdS2 x S2 x T7
• Holography of Non-relativistic String on AdS5xS5
• Action, Hamiltonian and CFT for 2D black holes
• AdS Solutions of 2D Type 0A
• AdS2/CFT1, Whittaker vector and Wheeler-De Witt equation
• Quantized Einstein-Rosen waves, AdS_2, and spontaneous symmetry breaking
• Superconformal Quantum Mechanics from M2-branes
• Raiders of the Lost AdS
• $Q\bar{Q}$ potential in the Schwinger model on curved space - time
• Three point functions and the effective lagrangian for the chiral primary fields in D=4 supergravity on AdS2 x S2
• Near horizon superconformal symmetry of rotating BPS black holes in five dimensions