We study the non-commutative instanton solution proposed in hep-th/0009142 and obtain the spectrum of small oscillations. The spectrum thus obtained is in exact agreement with the spectrum of stringy excitations in a configuration of point like D0 branes sitting on top of D4-branes with a uniform magnetic field turned on in the world-volume of the D4-branes in the Seiberg-Witten decoupling limit. This provides further evidence for the solution of hep-th/0009142 and also enables us recover the ADHM data from the 0-4 string spectrum. Generalizations to higher co-dimension solitons are also discussed.

As we have remarked earlier, it is rather remarkable that an intrinsically quantum concept such as entanglement has a very simple geometric dual. Part of the reason of course is that for planar field theories with ceff ≫ 1, one essentially attains a classical limit. Nevertheless, it is intriguing that there is a close connection between geometric concepts in the bulk and quantum features of the boundary theory. One therefore naturally wonders whether this fact can be leveraged to learn how the holographic map between quantum field theories and gravitational dynamics actually works.

The (planar) AdS Dirichlet problem has previously been shown to exhibit superluminal hydrodynamic sound modes. This problem is defined by bulk gravitational dynamics with Dirichlet boundary conditions imposed on a rigid timelike cut-off surface. We undertake a careful examination of this set-up and argue that, in most cases, the propagation of information between points on the Dirichlet hypersurface is nevertheless causal with respect to the induced light cones. In particular, the high-frequency dynamics is causal in this sense. There are however two exceptions and both involve boundary gravitons whose propagation is not constrained by the Einstein equations. These occur in i) AdS 3, where the boundary gravitons generally do not respect the induced light cones on the boundary, and ii) Rindler space, where they are related to the infinite speed of sound in incompressible uids. We discuss implications for the uid/gravity correspondence with rigid Dirichlet boundaries and for the black hole membrane paradigm. © SISSA 2012.

We explore entanglement negativity, a measure of the distillable entanglement contained in a quantum state, in relativistic field theories in various dimensions. We first give a general overview of negativity and its properties and then explain a well known result relating (logarithmic) negativity of pure quantum states to the Rényi entropy (at index 1/2), by exploiting the simple features of entanglement in thermal states. In particular, we show that the negativity of the thermofield double state is given by the free energy difference of the system at temperature T and 2 T respectively. We then use this result to compute the negativity in the vacuum state of conformal field theories in various dimensions, utilizing results that have been derived for free and holographic CFTs in the literature. We also comment upon general lessons to be learnt about negativity in holographic field theories.

The holographic RT and HRT prescriptions allow us to explore general properties of entanglement entropy in a class of QFTs. We will first examine the consistency of holographic entanglement entropy with expectations that follow from the basic definition as detailed in Sect. 2.4 We will also see that there are certain features that are peculiar to holographic systems, in part owing to the fact that we are working in the large ceff limit. We reiterate that the holographic entanglement entropy prescriptions are geared to capturing the leading semiclassical part of entanglement in terms of geometric data. Subleading corrections require ascertaining the bulk entanglement, as discussed in the previous section. All in all, this leads to some unexpected features, which at first sight seem unconventional, but are easily understood once one fully appreciates the implications of the limit ceff ≫ 1 being effectively a semiclassical regime of the QFT.

The black hole final state proposal implements manifest unitarity in the process of black hole formation and evaporation in quantum gravity, by postulating a unique final state boundary condition at the singularity. We argue that this proposal can be embedded in the gauge/gravity context by invoking a path integral formalism inspired by the Schwinger-Keldysh like thermo-field double construction in the dual field theory. This allows us to realize the gravitational quantum channels for information retrieval to specific deformations of the field theory path integrals and opens up new connections between geometry and information theory.

Scalar solitons in global AdS4 are holographically dual to coherent states carrying a non-trivial condensate of a scalar operator. We study the holographic information content of these states, focusing on a particular spatial region, by examining the entanglement entropy and causal holographic information. We show generically that whenever the dimension of the condensed operator is sufficiently low (characterized by the double-trace operator becoming relevant), such coherent states have lower entanglement and causal holographic information than the vacuum state of the system, despite having greater energy. We also use these geometries to illustrate the fact that causal wedges associated with a simply-connected boundary region can have non-trivial topology even in causally trivial spacetimes. © 2014 The Author(s).

Using measures of entanglement such as negativity and tangles we provide a detailed analysis of entanglement structures in pure states of non-interacting qubits. The motivation for this exercise primarily comes from holographic considerations, where entanglement is inextricably linked with the emergence of geometry. We use the qubit systems as toy models to probe the internal structure, and introduce some useful measures involving entanglement negativity to quantify general features of entanglement. In particular, our analysis focuses on various constraints on the pattern of entanglement which are known to be satisfied by holographic sates, such as the saturation of Araki-Lieb inequality (in certain circumstances), and the monogamy of mutual information. We argue that even systems as simple as few non-interacting qubits can be useful laboratories to explore how the emergence of the bulk geometry may be related to quantum information principles.

A simple but quite non-trivial class of non-equilibrium processes of a quantum many-body system is quantum quenches. We start with a ground state | φ0⟩ of a certain Hamiltonian H0. At time t = 0, we suddenly change the Hamiltonian from H0 to a new one H. The original state | φ0⟩ no longer stays at the ground state and starts to experience the time evolution for t > 0. Such a process is called a quantum quench. In particular, when the Hamiltonian changes homogeneously over the whole space, it is called a global quench [131, 132, 133], while if the change is localized in a certain small region, it is called a local quench [134].

We consider parity-odd transport in 2+1 dimensional charged fluids restricting attention to the class of non-dissipative fluids. We show that there is a two parameter family of such non-dissipative fluids which can be derived from an effective action, in contradistinction with a four parameter family that can be derived from an entropy current analysis. The effective action approach allows us to extract the adiabatic transport data, in particular the Hall viscosity and Hall conductivity amongst others, in terms of the thermodynamic functions that enter as 'coupling constants'. Curiously, we find that Hall viscosity is forced to vanish, whilst the Hall conductivity is generically a non-vanishing function of thermodynamic data determined in terms of the hydrodynamic couplings © SISSA 2013.