Introduction to the AdS/CFT correspondence
Introduction to the AdS/CFT correspondence
Introduction to the AdS/CFT correspondence
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12/22<br />
Partition functions. 6.<br />
<br />
<br />
To compute <strong>the</strong> path integral for <strong>the</strong> scalar<br />
field ϕ with <strong>the</strong> prescribed b.c. we calculate<br />
<strong>the</strong> value of <strong>the</strong> action S on <strong>the</strong> solution:<br />
S <br />
»<br />
»<br />
d D x B µ p ? ¡g g µν φB ν φq <br />
¡ d D x 1 Bϕ<br />
ɛD¡1ϕ Bz<br />
³ | zɛ<br />
For z Ñ 0 we have <strong>the</strong> asymp<strong>to</strong>tics<br />
ϕ Ñ z ∆ ¡ ϕ 0 pxq z ∆ d 4 y ϕ 0pyq<br />
2∆ , so<br />
|x¡y|<br />
S div.terms ¡<br />
»<br />
d 4 x d 4 y ϕ 0pxq ϕ 0 pyq<br />
|x ¡ y| 2∆
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