Entropy functional and the holographic attractor mechanism

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.

Aspects of AdS2 classification in M-theory: solutions with mesonic and baryonic charges

“…Having such full interpolating solutions from the near horizon to the asymptotically AdS 4 region would help clarify various aspects. For example, by evaluating its on-shell action one could potentially clarify the I-extremizaiton procedure [37][38][39] in terms of an attractor mechanism in the bulk extending on previous related work along the lines of [41][42][43].…”

The BPS limit of rotating AdS black hole thermodynamics

“…where the metric on the conformal boundary reads in the non-rotating frame ds 2 bdry = − ∆ θ Ξ dt ′2 + dθ 2 g 2 ∆ θ + sin 2 θ dφ ′2 g 2 Ξ , (B.12) and ∆ θ , Ξ were given in (3.4). 22 Using these expressions we can evaluate the conserved charges E and J, associated with the symmetries generated by ∂ ∂t ′ and − ∂ ∂φ ′ , respectively. We obtain: where u = Ξ ∆ θ ∂ ∂t ′ is the unit, outward-pointing timelike vector and Σ bdry is the two-dimensional Cauchy surface at the boundary, with metric induced from (B.12).…”

AdS Q-soliton and inhomogeneously mass-deformed ABJM model

“…On the other hand, we need holographic renormalization [32][33][34] to evaluate various physical quantities in the dual field theory. See [12,35] for closer applications to this work. Such quantities are determined by the asymptotic behavior of the fields.…”

“…This is the signal for the confinement-deconfinement phase transition in the dual quantum field theory [30]. Figure 5:H(r * ) andl(r * ) for a connected surface : Here the dimensionless quantities are defined in (35).…”

“…Naturally, r (r) over the range r < r 0 in (31) is always divergent at r * = r 0 . 7l is defined in(35).…”