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Register a new userThree-Dimensional Extremal Black Holes and the Maldacena Duality
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We discuss the microscopic states of the extremal BTZ black holes. Degeneracy of the primary states corresponding to the extremal BTZ black holes in the boundary N=(4,4) SCFT is obtained by utilizing the elliptic genus and the unitary representation theory of N=4 SCA. The degeneracy is consistent with the Bekenstein-Hawking entropy.
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Cold interacting fermions in two dimensions form exactly solvable Luttinger liquids, whose characteristic scaling exponents differ from those of conventional Fermi liquids. We use the AdS/CFT correspondence to discuss an equivalence between a class of helical, strongly coupled Luttinger liquids and fermions propagating in the background of a 3D black hole. The microscopic Lagrangian is explicitly known and the construction is fully embeddable in string theory. The retarded Green function at low temperature and energy arises from the geometry very near the black hole horizon. This structure is universal for all cold, charged liquids with a dual description in gravity.
We present a conformal isometry for static extremal black hole solutions in all four-dimensional Einstein-Maxwell-scalar theories with electromagnetic duality groups `of type $E_7$. This includes, but is not limited to, all supergravity theories with $mathcal{N}>2$ supersymmetry and all $mathcal{N}=2$ supergravity theories with symmetric scalar manifolds. The conformal isometry is valid for arbitrary electromagnetic charge configurations and relies crucially on the notion of Freudenthal duality.
Kerr/CFT correspondence has been recently applied to various types of 5D extremal rotating black holes. A common feature of all such examples is the existence of two chiral CFT duals corresponding to the U(1) symmetries of the near horizon geometry. In this paper, by studying the moduli space of the near horizon metric of five dimensional extremal black holes which are asymptotically flat or AdS, we realize an SL(2,Z) modular group which is a symmetry of the near horizon geometry. We show that there is a lattice of chiral CFT duals corresponding to the moduli points identified under the action of the modular group. The microscopic entropy corresponding to all such CFTs are equivalent and are in agreement with the Bekenstein-Hawking entropy.
We discuss 1/2 BPS domain walls in the 3d $mathcal N=4$ supersymmetric gauge theory which is self-dual under the 3d mirror symmetry. We find that if a BF-type coupling is introduced, invariance of the BPS domain wall under the duality transformation can be explicitly seen from the classical BPS equations. It has been known that particles and vortices are swapped under the 3d duality transformations. We show that Noether charges and vortex topological charges localized on the domain walls are correctly exchanged under the 3d mirror symmetry.
We review an explicit regularization of the AdS$_2$/CFT$_1$ correspondence, that preserves all isometries of bulk and boundary degrees of freedom. This scheme is useful to characterize the space of the unitary evolution operators that describe the dynamics of the microstates of extremal black holes in four spacetime dimensions. Using techniques from algebraic number theory to evaluate the transition amplitudes, we remark that the regularization scheme expresses the fast quantum computation capability of black holes as well as its chaotic nature.
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