Aitor Lewkowycz

Generalized gravitational entropy

A bstractWe consider classical Euclidean gravity solutions with a boundary. The boundary contains a non-contractible circle. These solutions can be interpreted as computing the trace of a density matrix in the full quantum gravity theory, in the classical approximation. When the circle is contractible in the bulk, we argue that the entropy of this density matrix is given by the area of a minimal surface. This is a generalization of the usual black hole entropy formula to euclidean solutions without a Killing vector.A particular example of this set up appears in the computation of the entanglement entropy of a subregion of a field theory with a gravity dual. In this context, the minimal area prescription was proposed by Ryu and Takayanagi. Our arguments explain their conjecture.

Quantum corrections to holographic entanglement entropy

A bstractWe consider entanglement entropy in quantum field theories with a gravity dual. In the gravity description, the leading order contribution comes from the area of a minimal surface, as proposed by Ryu-Takayanagi. Here we describe the one loop correction to this formula. The minimal surface divides the bulk into two regions. The bulk loop correction is essentially given by the bulk entanglement entropy between these two bulk regions. We perform some simple checks of this proposal.

Relative entropy equals bulk relative entropy

A bstractWe consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.

Exact results for the entanglement entropy and the energy radiated by a quark

A bstractWe consider a spherical region with a heavy quark in the middle. We compute the extra entanglement entropy due to the presence of a heavy quark both in

Deriving covariant holographic entanglement

\mathcal{N}

Observations on entanglement entropy in massive QFT’s

= 4 Super Yang Mills and in the

Universality in the geometric dependence of Rényi entropy

\mathcal{N}

Rényi entropy, stationarity, and entanglement of the conformal scalar

= 6 Chern-Simons matter theory (ABJM). This is done by relating the computation to the expectation value of a circular Wilson loop and a stress tensor insertion.We also give an exact expression for the Bremsstrahlung function that determines the energy radiated by a quark in the ABJM theory.

Bulk locality from modular flow

A bstractWe provide a gravitational argument in favour of the covariant holographic entanglement entropy proposal. In general time-dependent states, the proposal asserts that the entanglement entropy of a region in the boundary field theory is given by a quarter of the area of a bulk extremal surface in Planck units. The main element of our discussion is an implementation of an appropriate Schwinger-Keldysh contour to obtain the reduced density matrix (and its powers) of a given region, as is relevant for the replica construction. We map this contour into the bulk gravitational theory, and argue that the saddle point solutions of these replica geometries lead to a consistent prescription for computing the field theory Rényi entropies. In the limiting case where the replica index is taken to unity, a local analysis suffices to show that these saddles lead to the extremal surfaces of interest. We also comment on various properties of holographic entanglement that follow from this construction.

A CFT Perspective on Gravitational Dressing and Bulk Locality

A bstractWe identify various universal contributions to the entanglement entropy for massive free fields. As well as the ‘area’ terms found in [1], we find other geometric contributions of the form discussed in [2]. We also compute analogous contributions for a strongly coupled field theory using the AdS/CFT correspondence. In this case, we find the results for strong and weak coupling do not agree.