Scaling dimensions in hidden Kerr/CFT
David A. Lowe, Ilies Messamah, Antun Skanata
TL;DR
This paper explores how higher order corrections in Kerr black hole scattering relate to a hidden conformal field theory, revealing infinite towers of operators and the effects of symmetry breaking.
Contribution
It maps higher order wave equation corrections in Kerr backgrounds to CFT expansions, uncovering infinite primary operators and their running dimensions.
Findings
Infinite towers of CFT primary operators with positive dimensions.
Conformal symmetry is softly broken in Kerr backgrounds.
Scaling dimensions run with frequency, indicating symmetry breaking.
Abstract
It has been proposed that a hidden conformal field theory (CFT) governs the dynamics of low frequency scattering in a general Kerr black hole background. We further investigate this correspondence by mapping higher order corrections to the massless wave equations in a Kerr background to an expansion within the CFT in terms of higher dimension operators. This implies the presence of infinite towers of CFT primary operators with positive conformal dimensions compatible with unitarity. The exact Kerr background softly breaks the conformal symmetry and the scaling dimensions of these operators run with frequency. The scale-invariant fixed point is dual to a degenerate case of flat spacetime.
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