Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2007.02987

Effective entropy of quantum fields coupled with gravity

Xi Dong·Xiao-Liang Qi·Zhou Shangnan·Zhenbin Yang
View original source ↗Read source document ↗Export metadata ↓

Abstract

Entanglement entropy quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is well-defined for a fixed background geometry. In this paper, we propose a generalization of the quantum field theory entanglement entropy by including dynamical gravity. The generalized quantity named effective entropy, and its Renyi entropy generalizations, are defined by analytic continuation of a gravitational path integral on replica geometry with a co-dimension-$2$ brane at the boundary of region we are studying. We discuss different approaches to define the region in a gauge invariant way, and show that the effective entropy satisfies the quantum extremal surface formula. When the quantum fields carry a significant amount of entanglement, the quantum extremal surface can have a topology transition, after which an entanglement island region appears. Our result generalizes the Hubeny-Rangamani-Takayanagi formula of holographic entropy (with quantum corrections) to general geometries without asymptotic AdS boundary, and provides a more solid framework for addressing problems such as the Page curve of evaporating black holes in asymptotic flat spacetime. We apply the formula to two example systems, a closed two-dimensional universe and a four-dimensional maximally extended Schwarzchild black hole. We discuss the analog of the effective entropy in random tensor network models, which provides more concrete understanding of quantum information properties in general dynamical geometries. By introducing ancilla systems, we show how quantum information in the entanglement island can be reconstructed in a state-dependent and observer-dependent map. We study the closed universe (without spatial boundary) case and discuss how it is related to open universe.

Explore related subjects

hep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Xi Dong, Xiao-Liang Qi, Zhou Shangnan, Zhenbin Yang. 2020-07-06. Effective entropy of quantum fields coupled with gravity. https://doi.org/10.1007/jhep10(2020)052

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Gaillard-Zumino non-invertible symmetries

We uncover an infinite class of novel zero-form non-invertible symmetries in a broad family of four-dimensional models, studied years ago by Gaillard and Zumino (GZ), which includes several extended supergravities as particular subcases. The GZ models consist of abelian gauge fields coupled to a neutral sector, typically including a set of scalars, whose equations of motion are classically invariant under a continuous group $\mathscr{G}$ acting on the electric and magnetic field strengths via symplectic transformations. The standard lore holds that, at the quantum level, these symmetries are broken to an integral subgroup $\mathscr{G}_\mathbb{Z}$. We show that, in fact, a much larger subgroup $\mathscr{G}_\mathbb{Q}$ survives, albeit through non-invertible topological defects. We explicitly construct these defects and compute some of their fusion rules. As illustrative examples, we consider the axion-dilaton-Maxwell model and the bosonic sector of a class of $\mathcal{N}=2$ supergravities of the kind that appear in type II Calabi-Yau compactifications. Finally, we comment on how (part of) these non-invertible zero-form symmetries can be broken by gauging the $\mathscr{G}_\mathbb{Z}$ subgroup of invertible symmetries.

hep-th↗
arXiv2026

On the resolution of categorical symmetries in (Non-) Unitary Rational CFTs

We explore several aspects of categorical symmetry-resolved entanglement entropy (SREE) directly within two-dimensional rational conformal field theory (RCFT) (without invoking any SymTFT construction arXiv:2409.02806). We derive a general formula applicable whenever the action of the relevant topological defect lines on the annulus Hilbert space is known. This framework accommodates weakly and strongly symmetric boundaries, cloaking states, and fusion rings with multiplicities. We verify the formula in a range of diagonal unitary and non-unitary examples, including theories with generalized Haagerup-Izumi modular data. Furthermore, we extend the analysis to non-diagonal RCFTs. The $\frac{1}{2}E_6$ example demonstrates that closed-channel modular data and NIM-rep multiplicities alone do not suffice to determine the defect action on the complete open-channel Hilbert space.

hep-th↗
arXiv2026

Reflecting boundary conditions in critical loop models

In critical loop models, we call a boundary sticky if loops can attach to it, and reflecting otherwise. Using analytic bootstrap methods, we show that reflecting boundaries are characterised by one complex parameter, analogous to the boundary cosmological constant in Liouville theory. We determine disc 1-point functions, and write an explicit formula for disc 2-point functions as infinite combinations of conformal blocks. We also sketch the lattice interpretation of reflecting boundaries.

hep-th↗