Related papers: Cosmology meets cluster algebra
We identify cluster algebras for planar kinematics of conformal Feynman integrals in four dimensions, as sub-algebras of that for top-dimensional $G(4,n)$ corresponding to $n$-point massless kinematics. We provide evidence that they encode…
In this paper, we explore the cluster algebras for symbol letters or singularities of cosmological correlators in a conformally coupled scalar field theory. We show that the symbol letters for tree-level n-site ladder cosmological…
This paper presents an evaluation of the wave function coefficients for conformally coupled scalars at both one and two-loop levels at leading order in the coupling constant, in momentum space. We take cues from time-dependent interactions…
We uncover a combinatorial structure governing the differential equations satisfied by wavefunction coefficients of scalar fields with generic masses in de Sitter space. Using an integral representation of the massive mode functions, we…
We study cluster algebras for some all-loop Feynman integrals, including box-ladder, penta-box-ladder, and (seven-point) double-penta-ladder integrals. In addition to the well-known box ladder whose symbol alphabet is $D_2\simeq A_1^2$, we…
Motivated by the recent discovery of hidden zeros in particle and string amplitudes, we characterize zeros of individual graph contributions to the cosmological wavefunction of a scalar field theory. We demonstrate that these contributions…
The correlators of large-scale fluctuations belong to the most important observables in modern cosmology. Recently, there have been considerable efforts in analytically understanding the cosmological correlators and the related wavefunction…
Factorization homology theories of topological manifolds, after Beilinson, Drinfeld and Lurie, are homology-type theories for topological $n$-manifolds whose coefficient systems are $n$-disk algebras or $n$-disk stacks. In this work we…
In this paper we analyse the topological group cohomology of finite-dimensional Lie groups. We introduce a technique for computing it (as abelian groups) for torus coefficients by the naturally associated long exact sequence. The upshot in…
We extend the investigation of the structure of the late-time wavefunction of the universe to a class of toy models of scalars with time-dependent masses and polynomial couplings, which contains general massive scalars in FRW cosmologies.…
We derive for Bohmian mechanics topological factors for quantum systems with a multiply-connected configuration space Q. These include nonabelian factors corresponding to what we call holonomy-twisted representations of the fundamental…
For a FRW-spacetime coupled to an arbitrary real scalar field, we endow the solution space of the associated Wheeler-DeWitt equation with a Hilbert-space structure, construct the observables, and introduce the physical wave functions of the…
Significant progress has been made in our understanding of the analytic structure of FRW wavefunction coefficients, facilitated by the development of efficient algorithms to derive the differential equations they satisfy. Moreover, recent…
The wavefunction in quantum field theory is an invaluable tool for tackling a variety of problems, including probing the interior of Minkowski spacetime and modelling boundary observables in de Sitter spacetime. Here we study the analytic…
Motivated by the cluster structure of two-loop scattering amplitudes in N=4 Yang-Mills theory we define "cluster polylogarithm functions". We find that all such functions of weight 4 are made up of a single simple building block associated…
We give an explicit, rigorous framework for calculating quantum probabilities in a model theory of quantum gravity. Specifically, we construct the decoherence functional for the Wheeler-DeWitt quantization of a flat…
The cosmological polytope and bootstrap programs have revealed interesting connections between positive geometries, modern on-shell methods and bootstrap principles studied in the amplitudes community with the wavefunction of the Universe…
We interpret certain Seiberg-like dualities of two-dimensional N=(2,2) quiver gauge theories with unitary groups as cluster mutations in cluster algebras, originally formulated by Fomin and Zelevinsky. In particular, we show how the…
We apply the technique of standard supersymmetric factorization for any q factor ordering in the Wheeler-DeWitt (WDW) equation for barotropic Friedmann-Robertson-Walker (FRW) minisuperspace model, including the cosmological term. The…
In this text, we investigate webs which can be associated to cluster algebras from the point of view of the abelian functional equations these webs carry, focusing on the polylogarithmic ones. We introduce a general notion of webs whose…