de Sitter space and Holography
de Sitter space and Holography
de Sitter space and Holography
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g mn → f 2 g mnX → f −d−2 2 X√ −g → fd √ −g− √ −g(∂X) 2 → − √ −g(∂X) 2 − √ −g (d−2)2X 2 (∇ 2 ω)− √ −g (d−2)24X 2 (∇ω) 2√ −gR → fd−2 √ −g(R − 2(d − 1)(∇ 2 ω)−(d − 2)(d − 1)(∇ω) 2 )− √ −gξRX 2 → − √ −gξRX 2 + 2 √ −gξ(d − 1)(∇ 2 ω)+ √ −gξ(d − 2)(d − 1)(∇ω) 2−2 √ −gΛ → −2f d√ −gΛTable 1: Transformations un<strong>de</strong>r conformal rescaling;f = tanhz, ω = log f51