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