Related papers: De Sitter holographic complexity from Krylov compl…
We compute the length of spacelike geodesics anchored at opposite sides of certain double-sided flow geometries in two dimensions. These geometries are asymptotically anti-de Sitter but they admit either a de Sitter or a black hole event…
The observable universe has undergone periods of expansion that are well approximated by de Sitter (dS) space. Still lacking is a quantum mechanical description of dS, both globally and when restricted to the static patch. We develop a…
We study the properties of the double-scaled SYK (DSSYK) model under chord Hamiltonian deformations based on finite cutoff holography for general dilaton gravity theories with Dirichlet boundaries. The formalism immediately incorporates a…
Entanglement, chaos, and complexity are as important for de Sitter space as for AdS and for black holes. There are similarities and great differences between AdS and dS in how these concepts are manifested in the space-time geometry. In the…
A long-standing and intriguing question is: does the holographic principle apply to cosmologies like de Sitter spacetime? In this work, we consider a half dS spacetime wherein a timelike boundary encloses the bulk spacetime, presenting a…
This thesis explores the thermodynamics of the cosmological horizon, aiming to make progress towards a better understanding of the microscopic nature of its entropy. We utilise the constrained nature of low-dimensional gravity to do so and…
Building on the duality between Krylov complexity and geodesic length in Jackiw-Teitelboim and sine-dilaton gravity, we develop a precise holographic dictionary for quantities in the Krylov subspace of the double-scaled Sachdev-Ye-Kitaev…
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…
We study the CV, CA, and CV2.0 approaches to holographic complexity in $(d+1)$-dimensional de Sitter spacetime. We find that holographic complexity and corresponding growth rate presents universal behaviour for all three approaches. In…
We consider the holographic complexity conjectures for de-Sitter invariant states in a quantum field theory on de Sitter space, dual to asymptotically anti-de Sitter geometries with de Sitter boundaries. The bulk holographic duals include…
The cosmological horizon has an associated entropy suggesting that it might encode a quantum mechanical system on its surface. This has motivated extending the principles of the anti-de Sitter (AdS) space/ conformal field theory (CFT)…
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…
We investigate entanglement entropy between the pair of type II$_1$ algebras of the double-scaled SYK (DSSYK) model given a chord state, its holographic interpretation as generalized horizon entropy; particularly in the (anti-)de Sitter…
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…
We study holographic Krylov complexity in the Anabalon-Ross solitonic background, a top-down Type IIB solution describing a twisted-circle compactification of ${\cal N}=4$ SYM that flows to a confining, gapped three-dimensional theory.…
One of the important open problems in quantum black hole physics is a dual interpretation of holographic complexity proposals. To date the only quantitative match is the equality between the Krylov spread complexity in triple-scaled SYK at…
This Thesis explores the notion of Krylov complexity as a probe of quantum chaos and as a candidate for holographic complexity. The first Part is devoted to presenting the fundamental notions required to conduct research in this area.…
We investigate Cauchy Slice Holography in de Sitter spacetime. By performing a $T^2$ deformation of a (bottom-up) dS/CFT model, we obtain a holographic theory living on flat Cauchy slices of de Sitter, for which time is an emergent…
In the framework of the static patch approach to de Sitter holography introduced in [arXiv:2109.14104], the growth of holographic complexity has a hyperfast behaviour, which leads to a divergence in a finite time. This is very different…
Warped dS$_3$ arises as a solution to topologically massive gravity (TMG) with positive cosmological constant $+1/\ell^2$ and Chern-Simons coefficient $1/\mu$ in the region $\mu^2 \ell^2 < 27$. It is given by a real line fibration over…