# On the Kerr-AdS/CFT correspondence

## TL;DR

This paper explores the connection between conformal blocks in four-dimensional CFT and scalar field propagation in Kerr-AdS5 spacetime, providing exact and approximate expressions for scattering coefficients using isomonodromy and Liouville theory.

## Contribution

It introduces a novel approach linking Kerr-AdS5 scalar scattering to conformal blocks via isomonodromy and Liouville theory, offering new analytical tools for AdS/CFT correspondence.

## Key findings

- Exact scattering coefficients expressed through $c=1$ chiral conformal blocks.
- Approximate coefficients derived from semi-classical Liouville conformal blocks.
- Conformal blocks have a meaningful interpretation in terms of Liouville vertex operators.

## Abstract

We review the relation between four-dimensional global conformal blocks and field propagation in ${\rm AdS_5}$. Following the standard argument that marginal perturbations should backreact in the geometry, we turn to the study of scalar fields in the generic Kerr-${\rm AdS_5}$ 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.