Introduction to the AdS/CFT correspondence
Introduction to the AdS/CFT correspondence
Introduction to the AdS/CFT correspondence
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4/22<br />
The <strong>AdS</strong> space. 2.<br />
<br />
The global coordinates<br />
Y ¡1 cosh prq cos ptq, Y 0 cosh prq sin ptq,<br />
Y 1 sinh prq cos pφq, Y 2 sinh prq sin pφq<br />
ds 2 ¡ cosh prq 2 dt 2 dr 2 sinh prq 2 dφ 2 ,<br />
r P r0, 8q, t P p¡8, 8q, φ P r0, 2πq<br />
A conformal rescaling ds 2 cosh prq 2 d˜s 2<br />
and change of coordinates<br />
w 2 arctan pe r q ¡ π produces a metric<br />
2<br />
d˜s 2 ¡dt 2 dw 2 sin pwq 2 dφ 2 where<br />
w P r0, π 2 s ñ Disc
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