Topological transport from a black hole

In this paper the low temperature zero-frequency transport in a 2+1-dimensional theory dual to a dyonic black hole is discussed. It is shown that transport exhibits topological features: the transverse electric and heat conductivities satisfy the Wiedemann-Franz law of free electrons; the direct heat conductivity is measured in units of the central charge of the dual CFT, while the direct electric conductivity vanishes; the thermoelectric conductivity is non-zero at vanishing temperature, while the linear in temperature behaviour, controlled by the Mott relation, is subleading. Provided that the entropy of the black hole, and the dual system, is non-vanishing at zero temperature, the observations indicate that the dyonic black hole describes a "classical" limit of a highly degenerate topological state, in which the black hole charge measures the density of excited non-abelian quasiparticles.Comment: 5 pages, 1 figur

Entanglement Classification from a Topological Perspective

Classification of entanglement is an important problem in Quantum Resource Theory. In this paper we discuss an embedding of this problem in the context of Topological Quantum Field Theories (TQFT). This approach allows classifying entanglement patterns in terms of topological equivalence classes. In the bipartite case a classification equivalent to the one by Stochastic Local Operations and Classical Communication (SLOCC) is constructed by restricting to a simple class of connectivity diagrams. Such diagrams characterize quantum states of TQFT up to braiding and tangling of the ``connectome.'' In the multipartite case the same restricted topological classification only captures a part of the SLOCC classes, in particular, it does not see the W entanglement of three qubits. Nonlocal braiding of connections may solve the problem, but no finite classification is attempted in this case. Despite incompleteness, the connectome classification has a straightforward generalization to any number and dimension of parties and has a very intuitive interpretation, which might be useful for understanding specific properties of entanglement and for design of new quantum resources.Comment: 18 pages, 1 figure, version accepted to PRD. Significantly updated text following comments of referee(s). Extra references adde

Toy Gravizap for Black Hole Redemption

In this note a topological realization of a quantum teleportation protocol is considered. In this realization the notion of (non-) locality is discrete and isotopy invariant, which gives an additional control of how quantum states can be transferred to causally disconnected regions. There is an entropy associated with the disconnected regions that characterizes different steps of the teleportation protocol and one can introduce an analog of the Page curve for the entropy of the Hawking radiation. A generalization of the topological protocol is described as a toy model of black hole evaporation, with a unitary Page curve behavior.Comment: 5 pages, 1 figur

Black Holes in AdS/BCFT and Fluid/Gravity Correspondence

A proposal to describe gravity duals of conformal theories with boundaries (AdS/BCFT correspondence) was put forward by Takayanagi few years ago. However interesting solutions describing field theories at finite temperature and charge density are still lacking. In this paper we describe a class of theories with boundary, which admit black hole type gravity solutions. The theories are specified by stress-energy tensors that reside on the extensions of the boundary to the bulk. From this perspective AdS/BCFT appears analogous to the fluid/gravity correspondence. Among the class of the boundary extensions there is a special (integrable) one, for which the stress-energy tensor is fluid-like. We discuss features of that special solution as well as its thermodynamic properties.Comment: 18 pages, 4 figures (7 pdf-files). Save and view with Adobe Reader if images appear corrupted in the browse