Introduction to the AdS/CFT correspondence
Introduction to the AdS/CFT correspondence
Introduction to the AdS/CFT correspondence
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7/22<br />
Partition functions<br />
<br />
<br />
The <strong>correspondence</strong> can be made more precise<br />
Gubser, Klebanov, Polyakov; Witten, 1998<br />
To every field ϕ in <strong>the</strong> bulk of <strong>AdS</strong> <strong>the</strong>re<br />
corresponds a local opera<strong>to</strong>r Opxq on <strong>the</strong><br />
boundary<br />
For example, g µν ô T µν , A µ ô J µ<br />
<br />
<br />
Moreover, xe i ³ d 4 x φ 0 pxq Opxq y Z bulk pφ 0 q<br />
— <strong>the</strong> partition function of <strong>the</strong> bulk <strong>the</strong>ory<br />
with <strong>the</strong> condition φ Ñ φ 0 at <strong>the</strong> boundary<br />
i<br />
»<br />
d 4 x A µ B pxq J µ pxq is gauge-invariant!
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