Quantization of a scalar field in two Poincaré patches of anti-de Sitter space and AdS/CFT
Two sets of modes of a massive free scalar field are quantized in a pair of Poincaré patches of Lorentzian anti-de Sitter (AdS) space, AdSd+1 (d≥2). It is shown that in Poincaré coordinates (r,t,x→), the two boundaries at r=±∞ are connected. When the scalar mass m satisfies a condition 0<ν=(d2/4)...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2014-09-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321314002053 |
| Summary: | Two sets of modes of a massive free scalar field are quantized in a pair of Poincaré patches of Lorentzian anti-de Sitter (AdS) space, AdSd+1 (d≥2). It is shown that in Poincaré coordinates (r,t,x→), the two boundaries at r=±∞ are connected. When the scalar mass m satisfies a condition 0<ν=(d2/4)+(mℓ)2<1, there exist two sets of mode solutions to Klein–Gordon equation, with distinct fall-off behaviors at the boundary. By using the fact that the boundaries at r=±∞ are connected, a conserved Klein–Gordon norm can be defined for these two sets of scalar modes, and these modes are canonically quantized. Energy is also conserved. A prescription within the approximation of semi-classical gravity is presented for computing two- and three-point functions of the operators in the boundary CFT, which correspond to the two fall-off behaviours of scalar field solutions. |
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| ISSN: | 0550-3213 1873-1562 |