Entropy functional and the holographic attractor mechanism

TL;DR

This paper links the attractor mechanism for AdS4 black holes to a field theory interpretation via the holographic effective action in twisted ABJM theory, showing extremization reproduces black hole entropy.

Contribution

It provides a novel field theory perspective on the attractor mechanism by relating the holographic quantum effective action to the black hole entropy functional.

Findings

Holographic effective action matches the entropy functional.

Extremizing the effective action reproduces black hole entropy.

Field theory interpretation of the attractor mechanism established.

Abstract

We provide a field theory interpretation of the attractor mechanism for asymptotically AdS$_4$ dyonic BPS black holes whose entropy is captured by the supersymmetric index of the twisted ABJM theory at Chern-Simons level one. We holographically compute the renormalized off-shell quantum effective action in the twisted ABJM theory as a function of the supersymmetric fermion masses and the arbitrary vacuum expectation values of the dimension one scalar bilinear operators and show that extremizing the effective action with respect to the vacuum expectation values of the dimension one scalar bilinears is equivalent to the attractor mechanism in the bulk. In fact, we show that the holographic quantum effective action coincides with the entropy functional and, therefore, its value at the extremum reproduces the black hole entropy.