Cluster algebras for cosmological correlators

TL;DR

This paper investigates the role of cluster algebras in understanding the symbol letters of cosmological correlators, revealing algebraic structures that can aid in their analytic bootstrap.

Contribution

It identifies specific cluster algebras governing the symbol letters of tree-level and one-loop cosmological correlators, providing new algebraic tools for their analysis.

Findings

Tree-level n-site ladder correlators are governed by A_{2(n-1)} cluster algebras.

One-loop bubble correlator symbol letters form a union of two A_3 cluster algebras.

Cluster algebra relations facilitate the bootstrap of cosmological correlators.

Abstract

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 correlators are governed by A_{2(n-1)} cluster algebras. Additionally, we demonstrate that the symbol letters for one-loop bubble cosmological correlator are an union of two A_3 cluster algebras. The algebras relations of letters will provide an important tool to bootstrap analytic cosmological correlators.