Related papers: Cost of holographic path integrals
The path integral of pure 3D gravity with negative cosmological constant is formulated on a finite region of spacetime $M$, with boundary conditions that fix geodesic lengths or dihedral angles on $\partial M$. In the dual CFT, this…
We consider ($d+n+1$)-dimensional solutions of Einstein gravity with constant negative curvature. Regular solutions of this type are expected to be dual to the ground states of ($d+n$)-dimensional holographic CFTs on $AdS_d\times S^n$.…
It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way…
Representations of propagators by means of path integrals over velocities are discussed both in nonrelativistic and relativistic quantum mechanics. It is shown that all the propagators can only be expressed through bosonic path integrals…
We construct a model of 3D quantum gravity based on abelian topological quantum field theory (TQFT), by defining the gravitational path-integral as a sum over all 3D topologies with genus-$g$ boundary $\Sigma_g$. The path-integral of an…
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple…
We introduce the geodesic complexity of a metric space, inspired by the topological complexity of a topological space. Both of them are numerical invariants, but, while the TC only depends on the homotopy type, the GC is an invariant under…
Consider a general path planning problem of a robot on a graph with edge costs, and where each node has a Boolean value of success or failure (with respect to some task) with a given probability. The objective is to plan a path for the…
The action growth proposal relates the holographic complexity to the value of the action on the Wheeler-de Witt patch. We introduce a new method of calculating the gravitational action using the "bulk" term, i.e. the part of the…
We present two different approaches to stochastic integration in frictionless model free financial mathematics. The first one is in the spirit of It\^o's integral and based on a certain topology which is induced by the outer measure…
We study the Euclidean path integral of higher spin gravity on $S^4$. Based on a one-loop analysis, we are led to a gluing formula expressing the $S^4$ path integral in terms of an underlying $S^3$ path integral. We view the three-sphere as…
We prove a geometric linearisation result for minimisers of optimal transport problems where the cost-function is strongly p-convex and of p-growth. Initial and target measures are allowed to be rough, but are assumed to be close to…
In this paper, we argue that holographic complexity should be a basis-dependent quantity. Computational complexity of a state is defined as a minimum number of gates required to obtain that state from the reference state. Due to this…
In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main…
Accurate gravity field calculations are necessary for landing on planets, moons, asteroids, minimoons, or other irregularly shaped bodies, but current methods become increasingly inaccurate and slow near the surface. We present high…
We carry out the nonperturbative canonical quantization of several types of cosmological models that have already been studied in the geometrodynamic formulation using the complex path-integral approach. We establish a relation between the…
The requirement of the existence of a holographic c-function for higher derivative theories is a very restrictive one and hence most theories do not possess this property. Here, we show that, when some of the parameters are fixed, the…
The monography considers the problem of constructing a Hamiltonian cycle in a complete graph. A rule for constructing a Hamiltonian cycle based on isometric cycles of a graph is established. An algorithm for constructing a Hamiltonian cycle…
In the three-dimensional anti-de Sitter spacetime/two-dimensional conformal field theory correspondence, we derive the imaginary-time path-integral of a non-relativistic particle in the anti-de Sitter bulk space, which is dual to the ground…
In quantum field theory the path integral is usually formulated in the wave picture, i.e., as a sum over field evolutions. This path integral is difficult to define rigorously because of analytic problems whose resolution may ultimately…