arXiv subjects

Alessandro Palazio

Publications and source records attributed to Alessandro Palazio.

3 recordsLinked to original sources

arXiv2026

Generalised Cluster Adjacency for Cosmology

In this paper we study the cluster algebraic properties of wavefunction coefficients for conformally coupled scalar theories in de Sitter cosmology. We show that the symbol of the wavefunction coefficient of the $n$-site path graph $P_n$ obeys a generalisation of cluster adjacency, where all letters in a given word belong to the same cluster of an $A_{2n-3}$ algebra, with certain additional constraints on the order of the letters. We call this property the ordered single cluster condition, and provide its physical interpretation. This condition is stronger than the usual cluster adjacency obeyed by neighbouring letters, and thereby constrains the symbol bootstrap far more tightly. We also show that for an arbitrary graph the alphabet carries a cluster-like structure, described by tubes and tubings on the graph, which allows for a similar bootstrap approach.

hep-th↗

arXiv2025

Cosmology meets cluster algebra

In this paper we explore the mathematical properties of wavefunction coefficients in power-law FRW cosmologies, and establish their relation to cluster algebras. We focus on the particular contributions to the wavefunction coefficient coming from the path Feynman graphs, and show that the singularities of the wavefunction associated with a $n$-site path graph are related to the $\mathcal{X}$-coordinates of the cluster algebra $A_{2n-2}$. To establish this relation, we consider the symbol of the de Sitter wavefunction coefficients and show that the letters appearing there are the region variables associated to tubings on the path graph. These variables can be rewritten as simplicial coordinates of the moduli space $\mathcal{M}_{0,2n+1}$ and therefore identified with the $\mathcal{X}$-coordinates of type-$A_{2n-2}$ cluster algebras. We use this result to compute the wavefunction coefficients in terms of cluster functions.

hep-th↗

arXiv2025

Canonical Differential Equations for Cosmology from Positive Geometries

Cosmological correlation functions are central observables in modern cosmology, as they encode properties of the early universe. In this paper, we derive novel canonical differential equations for wavefunction coefficients in power-law FRW cosmologies by combining positive geometries and the combinatorics of tubings of Feynman graphs. First, we establish a general method to derive differential equations for any function given as a twisted integral of a logarithmic differential form. By using this method on a natural set of functions labelled by tubings of a given Feynman diagram, we derive a closed set of differential equations in the canonical form. The coefficients in these equations are related to region variables with the same notion of tubings, providing a uniform combinatorial description of the system of equations. We provide explicit results for specific examples and conjecture that this approach works for any graph.

hep-th↗