Feynman integrals, geometries and differential equations

TL;DR

This paper discusses constructing a basis of master integrals for multi-loop banana integrals, revealing their connection to Calabi-Yau geometries and extending the class of Feynman integrals with simplified differential equations.

Contribution

It introduces a method to obtain an $ ext{ε}$-factorised differential equation basis for higher-loop banana integrals linked to Calabi-Yau manifolds, expanding previous geometric cases.

Findings

Successfully constructed an $ ext{ε}$-factorised basis for l-loop banana integrals.

Extended the geometric understanding of Feynman integrals beyond genus-zero and genus-one cases.

Connected multi-loop integrals to higher-dimensional Calabi-Yau geometries.

Abstract

In this talk we discuss the construction of a basis of master integrals for the family of the $l$-loop equal-mass banana integrals, such that the differential equation is in an $\varepsilon$-factorised form. As the $l$-loop banana integral is related to a Calabi-Yau $(l-1)$-fold, this extends the examples where an $\varepsilon$-factorised form has been found from Feynman integrals related to curves (of genus zero and one) to Feynman integrals related to higher-dimensional varieties.