Introduction to the AdS/CFT correspondence

Partition functions. 5.
Therefore we impose the condition
ϕpx, zq| zÑ0
Ñ z ∆¡ ϕ 0 pxq
To solve the equation with this b.c. one needs
to find a function Kp⃗x, ⃗y, zq — the
boundary-to-boundary propagator — with the
property Kp⃗x, ⃗y, zq| zÑ0
Ñ z ∆¡ δp⃗x ¡ ⃗yq .
Then the desired solution may be written as
ϕp⃗x, zq
»
d 4 y Kp⃗x, ⃗y, zq ϕ 0 pyq
Check that this function is
z ¨∆
K
z 2 p⃗x ¡ ⃗yq 2
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