Entropy functional and the holographic attractor mechanism

TL;DR

The paper provides a field-theoretic realization of the attractor mechanism for asymptotically AdS$_4$ dyonic BPS black holes by equating the bulk entropy functional with the renormalized, off-shell quantum effective action of the dual twisted ABJM theory. Using Hamilton–Jacobi theory, it derives a universal effective superpotential for static dyonic solutions and constructs SUSY-preserving holographic renormalization with precise boundary conditions for the vector-multiplet scalars. The key result is that extremizing this quantum effective action with respect to the dimension-one scalar operator VEVs reproduces the bulk attractor horizon data and yields the black hole entropy, including for magnetic, dyonic, and (potentially) rotating configurations. This provides a rigorous, boundary-based interpretation of the AdS attractor mechanism and tightens the link between the topologically twisted index and black hole microstates in the ABJM context. The work also clarifies renormalization scheme choices, Legendre transforms, and SUSY constraints necessary to relate field theory observables to gravitational thermodynamics, with explicit constructions for magnetic CK solutions and extensions to dyonic cases.

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.