Freudenthal Duality in Conformal Field Theory

TL;DR

This paper explores how Freudenthal duality relates different extremal Kerr-Newman black holes and their dual conformal field theories, showing that it preserves entropy while mapping between CFTs with different parameters.

Contribution

It demonstrates the effect of rotational Freudenthal duality on the dual CFTs of extremal black holes, revealing how it preserves entropy and alters CFT parameters.

Findings

RFD maps two different CFTs with same entropy but different temperatures and central charges.

The duality over-rotates in the non-rotating limit, indicating a spurious branch.

RFD preserves the Cardy entropy across the dual CFTs.

Abstract

Rotational Freudenthal duality (RFD) relates two extremal Kerr-Newman (KN) black holes (BHs) with different angular momenta and electric-magnetic charges, but with the same Bekenstein-Hawking entropy. Through the Kerr/CFT correspondence (and its KN extension), a four-dimensional, asymptotically flat extremal KN BH is endowed with a dual thermal, two-dimensional conformal field theory (CFT) such that the Cardy entropy of the CFT is the same as the Bekenstein-Hawking entropy of the KN BH itself. Using this connection, we study the effect of the RFD on the thermal CFT dual to the KN extremal (or doubly-extremal) BH. We find that the RFD maps two different thermal, two-dimensional CFTs with different temperatures and central charges, but with the same asymptotic density of states, thereby matching the Cardy entropy. We also discuss the action of the RFD on doubly-extremal rotating BHs, finding a spurious branch in the non-rotating limit, and determining that for this class of BH solutions the image of the RFD necessarily over-rotates.