The one-state statement for closed universes has sparked considerable discussion. In this paper, we examine its physical meaning in the context of the Hartle-Hawking state and de Sitter space. We argue that the one-state property of closed universes is fully compatible with the finite-dimensional quantum mechanics experienced by observers inside de Sitter space, and that this compatibility requires neither mixing of $\textit{α}$-sectors nor any modification of the rules of the gravitational path integral. The apparent tension is resolved by sharply distinguishing the baby-universe Hilbert space (the space of closed universes viewed from the $\textit{outside}$) from the bulk Hilbert space that governs quantum mechanics for an observer $\textit{inside}$ a single de Sitter universe.

United States

Ying Zhao

“It from Bit”: the Hartle-Hawking state and quantum mechanics for de Sitter observers

We demonstrate that all anti-self-dual Einstein metrics with non-zero cosmological constant Λ locally arise from solutions of a single second order PDE introduced by Lipstein and Nagy. We show how this equation fits into the heavenly formalism of Plebański, and establish a Lax pair. Finally we show how Plebański’s second heavenly equation arises in the limit as Λ → 0.

United Kingdom

Maciej Dunajski

Timothy Moy

Heavenly equations in de Sitter space

We compute the holographic complexity of conformal quantum fields in rigid global de Sitter spacetime (dS ) using the volume and action prescriptions. First we consider AdS spacetime in global dS foliations, and compute the complexity of the CFT supported on the global dS conformal boundary. Next, we consider CFT supported on a global dS (UV) brane embedded in AdS spacetime, and compute the holographic complexity in this brane set up. We compare and contrast the results in the two cases, as well as with related results in the literature obtained in alternative holographic set ups involving patches of de Sitter spacetime covered by static coordinates or conformal (Poincaré) coordinates.

India

Sanhita Parihar

Shubho Roy

Holographic complexity of conformal fields in global de Sitter spacetime

In $\textit{d}$-dimensional de Sitter spacetime, consistency of the perturbative expansion necessitates imposing all second-order gravitational constraints associated with the $\textit{SO}$(1, $\textit{d}$) isometry group, rather than restricting to the $\textit{ℝ}$ × $\textit{SO}$($\textit{d}$ − 1) subgroup, to address linearization instability [1]. Since generic de Sitter isometries do not preserve a fixed static patch, these constraints cannot be implemented within a fixed local algebra. In this paper, we develop a framework that consistently imposes all $\textit{SO}$(1, $\textit{d}$) constraints while incorporating multiple observers on arbitrary timelike geodesics. This is achieved by introducing the concept of $\textit{covariant observer}$, whose geodesic transforms covariantly under the isometry group. Upon quantization, the observer is described by a superposition of geodesics, with the associated static patches fluctuating, providing a quantum reference frame $\textit{L}$ ($\textit{SO}$(1, $\textit{d}$)). We realize this structure in an action model in which a particle carries a set of conserved charges, each one corresponding to a generator of de Sitter isometry group, which parametrize its geodesic and upon quantization lead to a fluctuating geodesic.

China

Bin Chen

Jie Xu

An algebra for covariant observers in de Sitter space

We study numerically an <italic>s</italic>-wave holographic superconductor arising from an anti-de Sitter-Einstein-Born-Infeld black hole with backreaction within the framework of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, exploring how superconducting properties can be tuned through the nonlinearity of electrodynamics and gravitational backreaction. By introducing a parameter <italic>G</italic> to control the strength of the backreaction, we investigate non-perturbatively how the properties of the superconductor evolve as backreaction increases. We find that for small values of <italic>G</italic>, increasing the nonlinearity of the Born&#8211;Infeld electrodynamics makes the formation of the condensate harder&#8212;consistent with previous results in the literature&#8212;whereas for values of <italic>G</italic> close to unity the opposite behavior emerges, with nonlinearity slightly facilitating condensate formation. This qualitative switch between weak and strong backreaction regimes is also reflected in the electrical conductivity, the holographic entanglement entropy in the superconducting phase, and the superconducting gap ratio <italic>&#969;<inf>g</inf></italic>/ <italic>T<inf>c</inf></italic>, which exhibits significant deviations from its so-called universal value as backreaction strengthens. Moreover, we perform a detailed analysis of the superfluid density and the penetration depth associated with the Meissner effect, finding that nonlinear electrodynamics can induce effects analogous to those observed experimentally in the doping of conventional superconductors.

Mexico

Uriel Elinos

Edgar Guzmán-González

Marco Maceda

Numerical study of the properties of a holographic superconductor from an anti-de Sitter-Einstein-Born-Infeld black hole with backreaction

We construct an infinite family of semiclassical de Sitter (dS) microstates, realized as backreacted geometries of dS spacetime with a constant tension thin-shell brane located behind the dS event horizon. We show that wormhole contributions to the semiclassical dS Euclidean gravitational path integral lead to universal nonperturbative overlaps among the semiclassical dS microstates. By evaluating the nonperturbative overlaps, we count the dimension of the Hilbert space spanned by the semiclassical dS microstates and find that it precisely equals the exponential of the Gibbons-Hawking entropy of the dS spacetime. Our construction thus provides a gravitational state-counting derivation for the Gibbons-Hawking entropy of dS spacetime.

Zhi Wang

Microscopic origin of the entropy of de Sitter spacetime

<p>The local physics of light scalar fields in de Sitter space is well described by classical random walks, as expressed through the framework of stochastic inflation. Recent work has clarified how this formalism arises from quantum field theory and the renormalization group (RG), allowing for corrections to this formalism to be determined order by order. Yet, this description is incomplete. For example, the quantum dynamics of these fields are expected to become important when determining the tail of the probability distribution for the fluctuations. In this paper, we develop the understanding of fields in de Sitter as a quantum walk in order to bridge the gap between the classical and quantum description. We use the framework of exact RG to calculate the evolution equation for the reduced density matrix of the long wavelength fields. This master equation provides the direct map from light fields to models of quantum walks. We show how to reduce the master equation to stochastic inflation, and provide a new understanding of how the higher-order corrections arise. In the process, we demonstrate that divergences and secular growth in de Sitter, for both light and heavy fields, can be absorbed by (dynamical) renormalization.</p>

Daniel Green

Kshitij Gupta

Quantum walks and exact RG in de Sitter space

The thermodynamic characteristics of the string cloud-enclosed Hayward Anti-de Sitter black hole (BH) are discussed. The study is carried out for a quasi-homogeneous structure derived by the Hayward-AdS BH encircled by cloud of strings using a Legendre-invariant method called Geometrothermodynamics (GTD). This approach facilitates the investigation of phase transitions by identifying the singularities of the curvature scalars, which aids in determining the phase transition patterns based on thermodynamic factors. In addition, we explore how the Hayward parameter <italic>l<inf>p</inf></italic> may be understood as a thermodynamic variable inside the quasi-homogeneous thermodynamic framework, focusing on how it could influence phase transitions, particularly those with heat capacity divergences.

Pakistan

Sayed Farooq Ahmed Shah

Safia Taj

Quasi-homogeneous geometrothermodynamics of Hayward anti-de Sitter black hole surrounded by a cloud of strings

There is a series of scalar models possessing reflectionless kinks whose linear perturbations are described by a Pöschl-Teller potential at integer level $\textit{σ}$. The cases $\textit{σ}$ = 1 and 2 are the well-known Sine-Gordon and $\textit{ϕ}$ double-well models. The $\textit{σ}$ = 3 kink has received relatively little attention because it exhibits a $\textit{ϕ}$ potential, whose third derivative diverges in the vacuum. In old-fashioned perturbation theory this yields a cubic interaction that diverges far from a kink. We nonetheless use this interaction to calculate the amplitudes and probabilities for incoming radiation to excite or de-excite one of the kink’s two shape modes. As each shape mode is localized about the kink, the leading order amplitudes are nonetheless finite. This suggests that the $\textit{σ}$ = 3 model is not pathological, but rather its mesons are quantum field theoretic extensions of Znojil’s bound states.

Italy

Hengyuan Guo

Jarah Evslin

Stefano Bolognesi

(De-)Exciting the third Pöschl-Teller kink

We investigate the divergent perturbative series of correlation functions for a massless, self-interacting scalar field in de Sitter space. First, we use our previously proposed method of autonomous equations to obtain finite time-dependent functions, and show that these functions approximate the time evolution of the correlation functions of the stochastic approach reasonably well. Second, we apply the technique of autonomous equations to the Borel–Le Roy transforms of correlation functions, and use solutions of these equations to perform Borel resummation. The results match the time evolution obtained in the stochastic picture substantially better. In addition, we propose an alternative method for extracting perturbative coefficients and provide a new derivation of our autonomous equation by truncating a system of Schwinger–Dyson-type differential equations.

Alexander Kamenshchik

Russia

Polina Petriakova

Armenia

Tereza Vardanyan

Taming the infrared in de Sitter space: autonomous equations, stochastic approach, and Borel resummation