Generalized gravitational entropy

We consider the entanglement entropy for a free U(1) theory in 3+1 dimensions in the extended Hilbert space definition. By taking the continuum limit carefully we obtain a replica trick path integral which calculates this entanglement entropy. The path integral is gauge invariant, with a gauge fixing delta function accompanied by a Faddeev -Popov determinant. For a spherical region it follows that the result for the logarithmic term in the entanglement, which is universal, is given by the a anomaly coefficient. We also consider the extractable part of the entanglement, which corresponds to the number of Bell pairs which can be obtained from entanglement distillation or dilution. For a spherical region we show that the coefficient of the logarithmic term for the extractable part is different from the extended Hilbert space result. We argue that the two results will differ in general, and this difference is accounted for by a massless scalar living on the boundary of the region of interest.

Section: Jhep02(2017)101mentioning

confidence: 57%

Entanglement entropy in (3 + 1)-d free U(1) gauge theory

Soni

Trivedi

2017

“…The RyuTakayanagi conjecture was later reduced to the original AdS/CFT relation by Lewkowycz and Maldacena [12]. However, it took until Van Raamsdonk's essay [13] before the full scale of the connection between quantum entanglement, as geometric glue, and quantum gravity began to be emerge.…”

Section: Jhep12(2016)055mentioning

confidence: 99%

Holographic fluctuations and the principle of minimal complexity

Chemissany

Osborne

2016

We discuss, from a quantum information perspective, recent proposals of Maldacena, Ryu, Takayanagi, van Raamsdonk, Swingle, and Susskind that spacetime is an emergent property of the quantum entanglement of an associated boundary quantum system. We review the idea that the informational principle of minimal complexity determines a dual holographic bulk spacetime from a minimal quantum circuit U preparing a given boundary state from a trivial reference state. We describe how this idea may be extended to determine the relationship between the fluctuations of the bulk holographic geometry and the fluctuations of the boundary low-energy subspace. In this way we obtain, for every quantum system, an Einstein-like equation of motion for what might be interpreted as a bulk gravity theory dual to the boundary system.

“…Inspired by [18] they argued that the correction to the EE at linear order in the strength of the backreaction (a combination of the brane tension and Newton's constant) can be computed by evaluating the variation in the probe brane action ((4.3) plus counterterms) with respect to changes in the induced metric with respect to a number n. The n refers to certain "replica" geometries which are the bulk extensions of the n-fold covers of the boundary which would be needed to compute the EE directly in the field theory using the replica trick. In general, these bulk replica geometries are hard to find.…”

Section: Methodsmentioning

confidence: 99%

“…This is not the case for flavour corrections to the EE, which are a topic of recent interest [10][11][12][13][14][15][16][17]. However, [13], building on [18], found a shortcut to the problem which does not require computing the backreaction. Their method is particularly convenient for spherical regions as one can exploit the map [19] from the EE to the thermal entropy on R×H d−1 , which is easily computed by the area of the horizon in a certain hyperbolic slicing of AdS.…”

Section: Jhep03(2016)172mentioning

confidence: 99%

Holographic entanglement entropy for massive flavours in dS 4

Vaganov

2016

We examine the holographic entanglement entropy of spherical regions in de Sitter space in the presence of massive flavour fields which are modelled by probe D7 branes in AdS 5 × S 5 . We focus on the finite part of the massive correction to the entropy in the limits of small mass and large mass that are separated by a phase transition between two topologically distinct brane embeddings. For small masses, it approaches the flat space result for small spheres, whereas for large spheres there is a term that goes as the log of the sphere radius. For large masses, we find evidence for a universal contribution logarithmic in the mass. In all cases the entanglement entropy is smooth as the sphere radius crosses the horizon.