  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.
