Related papers: $p$-adic AdS/CFT
Certain closed-universe big-bang/big-crunch cosmological spacetimes may be obtained by analytic continuation from asymptotically AdS Euclidean wormholes, as emphasized by Maldacena and Maoz. We investigate how these Euclidean wormhole…
We develop, in the AdS/CFT correspondence, a method to compute correlation functions when the CFT is governed by the Lindblad equation for open quantum systems, via the AdS theory. Using a simple example in AdS$_3$/CFT$_2$, we demonstrate…
Given primes $\ell\ne p$, we record here a $p$-adic valued Fourier theory on a local field over $\mathbf{Q}_\ell$, which is developed under the perspective of group schemes. As an application, by substituting rigid analysis for complex…
We present a general relation between celestial correlation functions in $d$-dimensions and Witten diagrams in $\left(d+1\right)$-dimensional Euclidean anti-de Sitter (EAdS) space, to all orders in perturbation theory. Contact diagram…
Using the fact that flat space with a boundary is related by a Weyl transformation to anti-de Sitter (AdS) space, one may study observables in boundary conformal field theory (BCFT) by placing a CFT in AdS. In addition to correlation…
This article extends our study of the geometry of the $p$-adic eigencurve at a point defined by a weight $1$ cuspform $f$ irregular at $p$ and having complex multiplication, and the implications in Iwasawa and in Hida theories. The novel…
In Lorentzian AdS/CFT there exists a mapping between local bulk operators and nonlocal CFT operators. In global AdS this mapping can be found through use of bulk equations of motion and allows the nonlocal CFT operator to be expressed as a…
We will study the AdS/CFT correspondence in an intermediate region between the strong form of this correspondence (string theory on AdS being dual to a boundary CFT), and the weak form of this correspondence (supergravity on AdS being dual…
An important insight from the study of AdS/CFT is that bulk locality can be derived from crossing symmetry of the boundary CFT. In this paper, we take the first steps in extending this statement to de Sitter background by demonstrating how…
We show that AdS amplitudes are CFT correlators to all orders in the loop expansion by showing that they obey the conformal Ward identities. In particular, we provide explicit formulas for the constants and functions of cross-ratios that…
We discuss various aspects of HKLL bulk reconstruction for the free scalar field in AdS$_{d+1}$. First, we consider the spacelike reconstruction kernel for the non-normalizable mode in global coordinates. We construct it as a mode sum. In…
We consider the HKLL bulk reconstruction procedure for $p-$form fields and graviton in empty AdS$_{d + 1}$. We derive spacelike bulk reconstruction kernels for the $p$-forms and the graviton in the Poinarc\'e patch of AdS$_{d+1}$. The…
On the space $\mathbb Q_p^n$, where $p\ne 2$ and $p$ does not divide $n$, we construct a p-adic counterpart of spherical coordinates. As applications, a description of homogeneous distributions on $\mathbb Q_p^n$ and a skew product…
We present a deep neural network representation of the AdS/CFT correspondence, and demonstrate the emergence of the bulk metric function via the learning process for given data sets of response in boundary quantum field theories. The…
We study the holographic dual of a topological symmetry operator in the context of the AdS/CFT correspondence. Symmetry operators arise from topological field theories localized on a subspace of the boundary CFT spacetime. We use bottom up…
We express the branch points cross ratio of Hyper-elliptic Mumford curves as quotients of p adic theta functions evaluated at the p adic period matrix
We study the large AdS radius limit of correlation functions in holographic defect CFTs. For two-point functions of operators inserted away from the defect, we derive a position space formula relating a certain scaling limit of the…
We define a holographic dual to the Donaldson-Witten topological twist of $\mathcal{N}=2$ gauge theories on a Riemannian four-manifold. This is described by a class of asymptotically locally hyperbolic solutions to $\mathcal{N}=4$ gauged…
The strong subadditivity is the most important inequality which entanglement entropy satisfies. Based on the AdS/CFT conjecture, entanglement entropy in CFT is equal to the area of the minimal surface in AdS space. It is known that a Wilson…
This article introduces a new kind of number systems on $p$-adic integers which is inspired by the well-known $3n+1$ conjecture of Lothar Collatz. A $p$-adic system is a piecewise function on $\mathbb{Z}_p$ which has branches for all…