Speaker
Description
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 (DEQ) they satisfy. Moreover, recent findings indicate that the twisted cohomology framework tied to the hyperplane arrangement of these twisted integrals overestimates the number of master integrals required for defining the physical DEQ system. In this talk, we show that the associated dual cohomology is automatically organized in a way that is ideal for understanding and exploiting the cut/residue structure of the FRW wavefunction coefficients. Specifically, the hyperplane arrangement of these FRW integrals is non-generic due to linear relations obeyed by the hyperplane polynomials. Utilizing this understanding, we develop a systematic approach to organize compatible sequential residues, which dictate the physical basis for any graph. The talk will focus on the reduction from 25 to 16 physical integrals in the case of the 3-site tree graph, with a brief discussion on extending this analysis to arbitrary n-site, ℓ-loop graphs via universal graphical rules.
