Cornering Gapless Quantum States via Their Torus Entanglement

Witczak-Krempa

2017

Phys. Rev. D

Self Cite

We study the universal contributions to the entanglement entropy (EE) of 2+1d and 3+1d holographic conformal field theories (CFTs) on topologically non-trivial manifolds, focusing on tori. The holographic bulk corresponds to AdS-soliton geometries. We characterize the properties of these regulator-independent EE terms as a function of both the size of the cylindrical entangling region, and the shape of the torus. In 2+1d, in the simple limit where the torus becomes a thin 1d ring, the EE reduces to a shape-independent constant 2γ. This is twice the EE obtained by bipartitioning an infinite cylinder into equal halves. We study the RG flow of γ by defining a renormalized EE that 1) is applicable to general QFTs, 2) resolves the failure of the area law subtraction, and 3) is inspired by the F-theorem. We find that the renormalized γ decreases monotonically at small coupling when the holographic CFT is deformed by a relevant operator for all allowed scaling dimensions. We also discuss the question of non-uniqueness of such renormalized EEs both in 2+1d and 3+1d.

“…a(θ) shares many connections with χ(θ) [45]. First, it is symmetric about π, a(2π − θ) = a(θ), and decreasing convex on (0, π], (II.1).…”

Section: A Relation To Corner Entanglementmentioning

confidence: 99%

Section: ≥ Lymentioning

confidence: 99%

“…In the former case, the θ → π limit is non-singular, which when combined with the reflection symmetry about θ = π, leads to the following expansion [45] …”

Section: Basic Properties Of Entanglement Entropy On Torimentioning

confidence: 99%

“…We note that nothing constrains the sign of χ(π), and it can be either positive, negative or zero. In the so-called "thin-slice" limit, θ → 0, we instead get the divergence [45] …”

Section: Basic Properties Of Entanglement Entropy On Torimentioning

confidence: 99%

Section: Basic Properties Of Entanglement Entropy On Torimentioning

confidence: 99%

See 3 more Smart Citations

Holographic torus entanglement and its renormalization group flow

Witczak-Krempa

2017

Phys. Rev. D

Self Cite

Aspects of N-partite information in conformal field theories

Agón

Andino

et al. 2023

J. High Energ. Phys.

We present several new results for the N-partite information, IN, of spatial regions in the ground state of d-dimensional conformal field theories. First, we show that IN can be written in terms of a single N-point function of twist operators. Using this, we argue that in the limit in which all mutual separations are much greater than the regions sizes, the N-partite information scales as IN ~ r−2N∆, where r is the typical distance between pairs of regions and ∆ is the lowest primary scaling dimension. In the case of spherical entangling surfaces, we obtain a completely explicit formula for the I4 in terms of 2-, 3- and 4-point functions of the lowest-dimensional primary. Then, we consider a three- dimensional scalar field in the lattice. We verify the predicted long-distance scaling and provide strong evidence that IN is always positive for general regions and arbitrary N for that theory. For the I4, we find excellent numerical agreement between our general formula and the lattice result for disk regions. We also perform lattice calculations of the mutual information for more general regions and general separations both for a free scalar and a free fermion, and conjecture that, normalized by the corresponding disk entanglement entropy coefficients, the scalar result is always greater than the fermion one. Finally, we verify explicitly the equality between the N-partite information of bulk and boundary fields in holographic theories for spherical entangling surfaces in general dimensions.

Holographic entanglement entropy for perturbative higher-curvature gravities

Camps

López

2021

J. High Energ. Phys.

The holographic entanglement entropy functional for higher-curvature gravities involves a weighted sum whose evaluation, beyond quadratic order, requires a complicated theory-dependent splitting of the Riemann tensor components. Using the splittings of general relativity one can obtain unambiguous formulas perturbatively valid for general higher-curvature gravities. Within this setup, we perform a novel rewriting of the functional which gets rid of the weighted sum. The formula is particularly neat for general cubic and quartic theories, and we use it to explicitly evaluate the corresponding functionals. In the case of Lovelock theories, we find that the anomaly term can be written in terms of the exponential of a differential operator. We also show that order-n densities involving nR Riemann tensors (combined with n−nR Ricci’s) give rise to terms with up to 2nR− 2 extrinsic curvatures. In particular, densities built from arbitrary Ricci curvatures combined with zero or one Riemann tensors have no anomaly term in their functionals. Finally, we apply our results for cubic gravities to the evaluation of universal terms coming from various symmetric regions in general dimensions. In particular, we show that the universal function characteristic of corner regions in d = 3 gets modified in its functional dependence on the opening angle with respect to the Einstein gravity result.