Abstract
In this paper we study the AdS/CFT correspondence in the operator formalism without assuming the GKPW relation. We explicitly show that the low energy spectrum of the large N limit of CFT, which is realized by a strong coupling gauge theory, is identical to the spectrum of the free gravitational theory in the global AdS spacetime under some assumptions which are expected to be valid. Thus, two theories are equivalent for the low energy region under the assumptions. Using this equivalence, the bulk local field is constructed and the GKPW relation is derived.
Highlights
Represents the time.1 This was initiated in [4, 5]
In this paper we study the AdS/CFT correspondence in the operator formalism without assuming the GKPW relation
We explicitly show that the low energy spectrum of the large N limit of CFT, which is realized by a strong coupling gauge theory, is identical to the spectrum of the free gravitational theory in the global AdS spacetime under some assumptions which are expected to be valid
Summary
As we will see later, this equation appears for the e.o.m. of the gauge fields and gravitons. The normalized solution for the e.o.m. is given with the Gauss’s hyper geometric function as ψnlm(ρ). If m2 + d2/4 ≥ 1 is satisfied, the solution correspond ∆ = d/2 − m2 + d2/4(< d/2 − 1). We will consider this case only in this paper for simplicity and take ∆ = d/2 + m2 + d2/4.8 Using the standard inner product,. In the GN → 0 limit we have the quantized free scalar field φ(t, ρ, Ω) =. The Hamiltonian such that [H , anlm] = −ωnl. We choose the constant shift of the Hamiltonian as H |0 = 0 where |0 is the vacuum, i.e. anlm|0 = 0
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