On the Kerr-AdS/CFT correspondence

Abstract

We review the relation between four-dimensional global conformal blocks and field propagation in $\mathrm{Ad}{\mathrm{S}}_5$. Following the standard argument that marginal perturbations should backreact in the geometry, we turn to the study of scalar fields in the generic Kerr-$\mathrm{Ad}{\mathrm{S}}_5$ 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.

JHEP3 style, 34 pages, 2 figures; Minor changes in the text and a corrected near-extremal radial monodromy calculation. Version accepted to JHEP

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