On the Kerr-AdS/CFT correspondence. (English) Zbl 1381.81104
Summary: We review the relation between four-dimensional global conformal blocks and field propagation in \(\mathrm{AdS}_{5}\). Following the standard argument that marginal perturbations should backreact in the geometry, we turn to the study of scalar fields in the generic Kerr-\(\mathrm{AdS}_{5}\) geometry. On one hand, the result for scattering coefficients can be obtained exactly using the isomonodromy technique, giving exact expressions in terms of \(c=1\) chiral conformal blocks. On the other hand, one can use the analogy between the scalar field equations to the Level 2 null field Ward identity in two dimensional Liouville field theory to write approximate expressions for the same coefficients in terms of semi-classical chiral Liouville conformal blocks. Surprisingly, the conformal block thus constructed has a well-behaved interpretation in terms of Liouville vertex operators.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 83C57 | Black holes |
| 83E30 | String and superstring theories in gravitational theory |
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