A physical basis for cosmological correlators from cuts

TL;DR

This paper develops a cohomological framework to better understand the analytic structure of cosmological wavefunction coefficients, enabling systematic organization of physical cuts and residues in FRW integrals.

Contribution

It introduces a dual cohomology approach that simplifies the analysis of FRW integrals and provides graphical rules for enumerating physical cuts without calculations.

Findings

Dual cohomology organizes FRW integral structure effectively.

Physical subspace characterized by factorization into flat space amplitudes.

Graphical rules efficiently enumerate physical cuts.

Abstract

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 findings indicate that the twisted cohomology of the associated hyperplane arrangement defining FRW integrals overestimates the number of integrals required to define differential equations for the wavefunction coefficient. We demonstrate that the associated dual cohomology is automatically organized in a way that is ideal for understanding and exploiting the cut/residue structure of FRW integrals. Utilizing this understanding, we develop a systematic approach to organize compatible sequential residues, which dictates the physical subspace of FRW integrals for any $n$-site, $\ell$-loop graph. In particular, the physical subspace of tree-level FRW wavefunction coefficients is populated by differential forms associated to cuts/residues that factorize the integrand of the wavefunction coefficient into only flat space amplitudes. After demonstrating the validity of our construction using intersection theory, we develop simple graphical rules for cut tubings that enumerate the space of physical cuts and, consequently, differential forms without any calculation.