arXiv subjects

Sergio E. Aguilar-Gutierrez

Publications and source records attributed to Sergio E. Aguilar-Gutierrez.

31 records · Page 2Linked to original sources

arXiv2024

Complexity = Anything Can Grow Forever in de Sitter

Recent developments in anti-de Sitter holography point towards the association of an infinite class of covariant objects, the simplest one being codimension-one extremal volumes, with quantum computational complexity in the microscopic description. One of the defining features of these gravitational complexity proposals is describing the persistent growth of black hole interior in classical gravity. It is tempting to assume that the gravitational complexity proposals apply also to gravity outside their native anti-de Sitter setting in which case they may reveal new truths about these cases with much less understood microscopics. Recent first steps in this direction in de Sitter static patch demonstrated a very different behavior from anti-de Sitter holography deemed hyperfast growth: diverging complexification rate after a finite time. We show that this feature is not a necessity and among gravitational complexity proposals there are ones, which predict linear or exponential late-time growth behaviors for complexity in de Sitter static patches persisting classically forever.

hep-th↗

arXiv2024

Towards complexity in de Sitter space from the double-scaled Sachdev-Ye-Kitaev model

How can we define complexity in dS space from microscopic principles? Based on recent developments pointing towards a correspondence between a pair of double-scaled Sachdev-Ye-Kitaev (DSSYK) models/ 2D Liouville-de Sitter (LdS$_2$) field theory/ 3D Schwarzschild de Sitter (SdS$_3$) space in arXiv:2310.16994, arXiv:2402.00635, arXiv:2402.02584, we study concrete complexity proposals in the microscopic models and their dual descriptions. First, we examine the spread complexity of the maximal entropy state of the doubled DSSYK model. We show that it counts the number of entangled chord states in its doubled Hilbert space. We interpret spread complexity in terms of a time difference between antipodal observers in SdS$_3$ space, and a boundary time difference of the dual LdS$_2$ CFTs. This provides a new connection between entanglement and geometry in dS space. Second, Krylov complexity, which describes operator growth, is computed for physical operators on all sides of the correspondence. Their late time evolution behaves as expected for chaotic systems. Later, we define the query complexity in the LdS$_2$ model as the number of steps in an algorithm computing n-point correlation functions of boundary operators of the corresponding antipodal points in SdS$_3$ space. We interpret query complexity as the number of matter operator chord insertions in a cylinder amplitude in the DSSYK, and the number of junctions of Wilson lines between antipodal static patch observers in SdS$_3$ space. Finally, we evaluate a specific proposal of Nielsen complexity for the DSSYK model and comment on its possible dual manifestations.

hep-th↗

arXiv2024

Holographic complexity of the extended Schwarzschild-de Sitter space

According to static patch holography, de Sitter space admits a unitary quantum description in terms of a dual theory living on the stretched horizon, that is a timelike surface close to the cosmological horizon. In this manuscript, we compute several holographic complexity conjectures in a periodic extension of the Schwarzschild-de Sitter black hole. We consider multiple configurations of the stretched horizons to which geometric objects are anchored. The holographic complexity proposals admit a hyperfast growth when the gravitational observables only lie in the cosmological patch, except for a class of complexity=anything observables that admit a linear growth. All the complexity conjectures present a linear increase when restricted to the black hole patch, similar to the AdS case. When both the black hole and the cosmological regions are probed, codimension-zero proposals are time-independent, while codimension-one proposals can have non-trivial evolution with linear increase at late times. As a byproduct of our analysis, we find that codimension-one spacelike surfaces are highly constrained in Schwarzschild-de Sitter space. Therefore, different locations of the stretched horizon give rise to different behaviours of the complexity conjectures.

hep-th↗

arXiv2024

Holographic complexity: braneworld gravity versus the Lloyd bound

We explore the complexity equals volume proposal for planar black holes in anti-de Sitter (AdS) spacetime in 2+1 dimensions, with an end of the world (ETW) brane behind the horizon. We allow for the possibility of intrinsic gravitational dynamics in the form of Jackiw-Teitelboim (JT) gravity to be localized on the brane. We compute the asymptotic rate of change of volume complexity analytically and obtain the full time dependence using numerical techniques. We find that the inclusion of JT gravity on the brane leads to interesting effects on time dependence of holographic complexity. We identify the region in parameter space (the brane location and the JT coupling) for which the rate of change of complexity violates the Lloyd bound. In an equivalent description of the model in terms of an asymptotically AdS wormhole, we connect the violation of the Lloyd bound to the violation of a suitable energy condition in the bulk that we introduce. We also compare the Lloyd bound constraints to previously derived constraints on the bulk parameters in this model that are based on bounds on entanglement growth in the dual CFT state.

hep-th↗

arXiv2024

Krylov complexity is not a measure of distance between states or operators

We ask whether Krylov complexity is mutually compatible with the circuit and Nielsen definitions of complexity. We show that the Krylov complexities between three states fail to satisfy the triangle inequality and so cannot be a measure of distance: there is no possible metric for which Krylov complexity is the length of the shortest path to the target state or operator. We show this explicitly in the simplest example, a single qubit, and in general.

hep-th↗

arXiv2024

The centaur-algebra of observables

This letter explores a transition in the type of von Neumann algebra for asymptotically AdS spacetimes from the implementations of the different gravitational constraints. We denote it as the \emph{centaur-algebra} of observables. In the first part of the letter, we employ a class of flow geometries interpolating between AdS$_2$ and dS$_2$ spaces, the centaur geometries. We study the type II$_\infty$ crossed product algebra describing the semiclassical gravitational theory, and we explore the algebra of bounded sub-regions in the bulk theory following $T\overline{T}$ deformations of the geometry and study the gravitational constraints with respect to the quasi-local Brown-York energy of the system at a finite cutoff. In the second part, we study arbitrary asymptotically AdS spacetimes, where we implement the boundary protocol of an infalling observer modeled as a probe black hole proposed by arXiv:2211.16512 to study modifications in the algebra. In both situations, we show how incorporating the constraints requires a type II$_1$ description.

hep-th↗

arXiv2024

C=Anything and the switchback effect in Schwarzschild-de Sitter space

We investigate observables within the framework of the codimension-one C=Anything (CAny) proposal for Schwarzschild-de Sitter (SdS) space under the influence of shockwave sources. Within the proposal, there is a set of time-reversal invariant observables that display the same rate of growth at early and late-times for a background with or without shockwave sources. Once we introduce shockwaves in the weak gravitational coupling regime, there is a decrease in the late-time complexity growth due to cancellations with early-time perturbations, known as the switchback effect. The result shows that some CAny observables in SdS may reproduce the same type of behavior found in anti-de Sitter black holes. We comment on how our results might guide us to new explorations in the putative quantum mechanical theory.

hep-th↗

arXiv2023

Axion-de Sitter wormholes

We construct wormholes supported by axion flux in the presence of a positive cosmological constant. The solutions describe compact, one-handle bodies colloquially known as kettlebell geometries. The wormholes are perturbatively stable, but regularity of the Euclidean geometry implies an upper bound on the axion flux. Viewed as no-boundary saddle points, wormholes are suppressed relative to the round sphere. The symmetric kettlebell with maximal axion density has vanishing Euclidean action. Continuing into the Lorentzian across the equator, the solutions describe two expanding branches of de Sitter space filled with an axion field that rapidly dilutes and connected by a quantum bounce across which the arrow of time reverses.

hep-th↗

arXiv2023

Entangled universes in dS wedge holography

We develop a new setting in the framework of braneworld holography to describe a pair of coupled and entangled uniformly accelerated universes. The model consists of two branes embedded into AdS space capping off the UV and IR regions, giving rise to a notion of dS wedge holography. Specializing in a three-dimensional bulk, we show that dS JT gravity can emerge as an effective braneworld theory, provided that fluctuations transverse to the brane are included. We study the holographic entanglement entropy between the branes as well as the holographic complexity within the `complexity=anything' proposal. We reproduce a Page curve with respect to an observer collecting radiation on the UV brane, as long as we take the limit where gravity decouples in that universe, thus acting as a non-gravitating bath. The Page curve emerges due to momentum-space (UV/IR) entanglement and can be understood as analogous to the `confinement-deconfinement' transition in theories with a mass gap. Moreover, the analysis of complexity shows that the hyperfast growth phenomenon is displayed within a set of proposals, while late-time linear growth can be recovered for a different set. Our framework thus provides new test grounds for understanding quantum information concepts in dS space and dS holography.

hep-th↗

arXiv2023

Aspects of higher-curvature gravities with covariant derivatives

We study various aspects of higher-curvature theories of gravity built from contractions of the metric, the Riemann tensor and the covariant derivative, $\mathcal{L}(g^{ab},R_{abcd},\nabla_a)$. We characterise the linearized spectrum of these theories and compute the modified Newton potential in the general case. Then, we present the first examples of Generalized Quasi-topological (GQT) gravities involving covariant derivatives of the Riemann tensor. We argue that they always have second-order equations on maximally symmetric backgrounds. Focusing on four spacetime dimensions, we find new densities of that type involving eight and ten derivatives of the metric. In the latter case, we find new modifications of the Schwarzschild black hole. These display thermodynamic properties which depart from the ones of polynomial GQT black holes. In particular, the relation between the temperature and the mass of small black holes, $T\sim M^{1/3}$, which universally holds for general polynomial GQT modifications of Einstein gravity, gets modified in the presence of the new density with covariant derivatives to $T\sim M^{3}$. Finally, we consider brane-world gravities induced by Einstein gravity in the AdS bulk. We show that the effective quadratic action for the brane-world theory involving arbitrary high-order terms in the action can be written explicitly in a closed form in terms of Bessel functions. We use this result to compute the propagator of metric perturbations on the brane and its pole structure in various dimensions, always finding infinite towers of ghost modes, as well as tachyons and more exotic modes in some cases.

hep-th↗

arXiv2023

An Outsider's Perspective on Information Recovery in de Sitter Space

Entanglement islands play a crucial role in our understanding of how Hawking radiation encodes information in a black hole, but their relevance in cosmological spacetimes is less clear. In this paper, we continue our investigation of information recovery in de Sitter space and construct a two-dimensional model of gravity containing a domain wall that interpolates between de Sitter space and Rindler space. The Rindler wedges introduce weakly-gravitating asymptotic regions from which de Sitter space can be probed, yielding an outside perspective of the cosmological horizon. In contrast to earlier works, backreaction effects are under control by considering a quantum state that only breaks the thermal equilibrium of the Bunch-Davies state for a finite time. This allows information to be decoded from the Gibbons-Hawking radiation in a controlled fashion.

hep-th↗

arXiv2022

Towards an "AdS$_1/$CFT$_0$" correspondence from the D$(-1)/$D$7$ system?

We argue that a type IIB Euclidean supergravity solution of the form $\mathbb{R}\times S^1\times \mathbb{T}^8$ with imaginary self-dual $F_1$ flux through $\mathbb{R}\times S^1$ belongs to the chain of $AdS_d\times S^d\times \mathbb{T}^{10-2d}$ vacua with (imaginary) self-dual $F_d$ flux, where $d\leq 5$. Such vacua come from the near-horizon of D$(d-2)$/D$(8-d)$ branes and are supersymmetric for odd values of $d$. For $d=1$ we speculate that the hallmark of conformal symmetry for the matrix model dual is a vanishing free energy. The matrix dual was recently constructed by arXiv:2101.01732 by adding matrix interactions coming from strings stretching between the D$(-1)$ and D$7$ branes to the IKKT matrix model. We find that the corresponding supergravity solution indeed has vanishing on-shell action. Specific $F_5$ fluxes need to be switched on as a consequence of (a T-dual version of) the Hanany-Witten effect.

hep-th↗

arXiv2022

Islands in Multiverse Models

We consider multiverse models in two-dimensional linear dilaton-gravity theories as toy models of false vacuum eternal inflation. Coupling conformal matter we calculate the Von Neumann entropy of subregions. When these are sufficiently large we find that an island develops covering most of the rest of the multiverse, leading to a Page-like transition. This resonates with a description of multiverse models in semiclassical quantum cosmology, where a measure for local predictions is given by saddle point geometries which coarse-grain over any structure associated with eternal inflation beyond one's patch.

hep-th↗