A correction to this paper has been published: https://doi.org/10.1007/JHEP04(2025)171

United States

Molly Kaplan

Donald Marolf

Xuyang Yu

Ying Zhao

Erratum to: De Sitter quantum gravity and the emergence of local algebras

Quantum theories of gravity are generally expected to have some degree of non-locality, with familiar local physics emerging only in a particular limit. Perturbative quantum gravity around backgrounds with isometries and compact Cauchy slices provides an interesting laboratory in which this emergence can be explored. In this context, the remaining isometries are gauge symmetries and, as a result, gauge-invariant observables cannot be localized. Instead, local physics can arise only through certain relational constructions.

De Sitter quantum gravity and the emergence of local algebras

Random tensor networks (RTNs) have proved to be fruitful tools for modelling the AdS/CFT correspondence. Due to their flat entanglement spectra, when discussing a given boundary region R and its complement   <math> <mover> <mi>R</mi> <mo>¯</mo> </mover> </math>  $$ \overline{R} $$ , standard RTNs are most analogous to fixed-area states of the bulk quantum gravity theory, in which quantum fluctuations have been suppressed for the area of the corresponding HRT surface. However, such RTNs have flat entanglement spectra for all choices of R,   <math> <mover> <mi>R</mi> <mo>¯</mo> </mover> </math>  $$ \overline{R} $$ , while quantum fluctuations of multiple HRT-areas can be suppressed only when the corresponding HRT-area operators mutually commute. We probe the severity of such obstructions in pure AdS3 Einstein-Hilbert gravity by constructing networks whose links are codimension-2 extremal-surfaces and by explicitly computing semiclassical commutators of the associated link-areas. Since d = 3, codimension-2 extremal-surfaces are geodesics, and codimension-2 ‘areas’ are lengths. We find a simple 4-link network defined by an HRT surface and a Chen-Dong-Lewkowycz-Qi constrained HRT surface for which all link-areas commute. However, the algebra generated by the link-areas of more general networks tends to be non-Abelian. One such non-Abelian example is associated with entanglement-wedge cross sections and may be of more general interest.

Jesse Held

China

Jie-qiang Wu

Link-area commutators in AdS3 area-networks

Due to the presence of a gravitational anomaly in topologically massive gravity (TMG), the geometric entropy is no longer simply the Hubeny-Rangamani-Takayanagi (HRT) area; instead, it is given by the HRT area plus an anomalous contribution. We study the action of this geometric entropy on the covariant phase space of classical solutions for TMG with matter fields whose action is algebraic in the metric. The result agrees precisely with the action of HRT area operators in Einstein-Hilbert gravity given in [8], i.e., it is a boundary-condition-preserving kink transformation. Furthermore, we show our result to be consistent with direct computations of semiclassical commutators of geometric entropies in pure TMG spacetimes asymptotic to planar AdS, as computed in [21].

The action of geometric entropy in topologically massive gravity

Recently, an increasing interest in UV/IR mixing phenomena has drawn attention to the range of validity of standard quantum field theory. Here we explore the consequences of such a limited range of validity in the context of radiative models for neutrino mass generation. We adopt an argument first published by Cohen, Kaplan and Nelson that gravity implies both UV and IR cutoffs, apply it to the loop integrals describing radiative corrections, and demonstrate that this effect has significant consequences for the parameter space of radiative neutrino mass models.

Germany

Patrick Adolf

Spain

Martin Hirsch

Heinrich Päs

Radiative neutrino masses and the Cohen-Kaplan-Nelson bound

We study the action of Hubeny-Rangamani-Takayanagi (HRT) area operators on the covariant phase space of classical solutions. It has been previously proposed that this action generates a transformation which, roughly speaking, boosts the entanglement wedge on one side of the HRT surface relative to the entanglement wedge on the other side. We give a sharp argument for a precise result of this form in a general theory of Einstein-Hilbert gravity minimally coupled to matter, taking appropriate care with asymptotically Anti-de Sitter (AdS) boundary conditions. The result agrees with direct computations of commutators involving HRT areas in pure 2+1 dimensional Einstein-Hilbert gravity on spacetimes asymptotic to planar AdS. We also clarify the sense in which this transformation is singular in the deep UV when the HRT-surface is anchored to an asymptotically AdS boundary.

The action of HRT-areas as operators in semiclassical gravity

The Cohen–Kaplan–Nelson (CKN) bound formulates the condition that black hole is not produced by the low energy effective field theory dynamics. In de Sitter space it also constrains the maximal size of the matter distribution to be smaller than the cosmological horizon determined by black hole. On the other hand, the swampland distance conjecture (SDC) predicts that de Sitter space becomes unstable by the descent of the low energy degrees of freedom from UV. This results in the rapid increase in the energy inside the cosmological horizon, the distribution of which can be constrained by the CKN bound. We study the CKN bound in de Sitter space in detail and point out that when compared with the slow-roll in the inflation, the bound on the slow-roll parameter which forbids the eternal inflation is obtained.

South Korea

Min-Seok Seo

Implication of the swampland distance conjecture on the Cohen–Kaplan–Nelson bound in de Sitter space

The holographic principle implies that quantum field theory (QFT) overcounts the number of independent degrees of freedom in quantum gravity. An argument due to Cohen, Kaplan, and Nelson (CKN) suggests that the number of degrees of freedom well described by QFT is even smaller than required by holographic bounds, and CKN interpreted this result as indicative of a correlation between the UV and IR cutoffs on QFT. Here, we consider an alternative interpretation in which the QFT degrees of freedom are depleted as a function of scale. We use a simple recipe to estimate the impact of depleted densities of states on precision observables, including the Lamb shift and lepton <math><mi>g</mi><mo>−</mo><mn>2</mn></math>. Although these observables are not sensitive to the level of depletion motivated by gravitational considerations, the phenomenological exercises also provide an interesting test of quantum field theory that is independent of underlying quantum gravity assumptions. A depleted density of states can also render the QFT vacuum energy UV insensitive, reconciling the success of QFT in describing ordinary particle physics processes and its apparent failure in predicting the cosmological constant.

Nikita Blinov

Patrick Draper

Densities of states and the Cohen-Kaplan-Nelson bound

Cohen, Kaplan, and Nelson (CKN) conjectured that the UV and IR cutoffs of effective quantum field theories coupled to gravity are not independent, but are connected by the physics of black holes. We interpret the CKN bound as a scale-dependent depletion of the quantum field theory (QFT) density of states and discuss various aspects of the bound on small and large scales. For laboratory experiments, we argue that the bound provides small corrections to ordinary quantum field theory, which we estimate to be of order <math><msub><mi>m</mi><mi>e</mi></msub><mo>/</mo><msub><mi>M</mi><mi>p</mi></msub></math> for <math><mi>g</mi><mo>−</mo><mn>2</mn></math> of the electron. On large scales, we suggest a modification of the CKN bound due to the presence of cosmological horizons and discuss the connection with entropy bounds.