Thimble decomposition and Wall Crossing Structure for Physical Integrals

by Roberta Angius (Hamburg U.)

Wednesday 26 Nov 2025, 14:30 → 16:30 Europe/Rome

1/1-2 - Aula "C. Voci" (Dipartimento di Fisica e Astronomia - Edificio Marzolo)

A growing body of evidence suggests that the complexity of physical integrals is most naturally
understood through geometry. Recent mathematical developments by Kontsevich and Soibelman
[arXiv:2402.07343] have illuminated the role of exponential integrals as periods of twisted de Rham
cocycles over Betti cycles, offering a structured approach to address this problem in a wide range
of settings. In this talk, I will first introduce the key tools underlying this structure and then apply
them to show how families of physically relevant integrals, ranging from holomorphic exponentials
to logarithmic multivalued functions, can be reformulated within this language. For holomorphic
exponents, I will present an explicit decomposition of a family of integrals into thimbles expansion
together with a detailed analysis of the wall-crossing structure behind the analytic continuation of
its relevant parameter. Finally, I will discuss the generalization to multivalued functions, which
provides the appropriate framework for describing Feynman integrals in special representations.
In this context, the thimble decomposition is expected to match the decomposition into Master
Integrals, while the study of the wall-crossing structure yields a precise count of independent Master
Integrals (or periods), circumventing complications arising from Stokes phenomena.