Welcome to the YITP workshop "Homotopy Algebra of Quantum Field Theory and Its Application", March 24 - 31 2021, in Kyoto and Online
Recently, homotopy algebra, such as A-infinity or L-infinity, has regained attention in the study of quantum field theory (QFT). In the context of string theory, it is known that an A-infinity or L-infinity algebra arises as a consistency condition that the interactions of strings must satisfy and is useful to study the S-matrix, effective theory with finite \alpha', RG flows and so on.
Actually, we can extract such a homotopy algebra from a given path-integrable QFT with the help of the Batalin-Vilkovisky (BV) formalism, which may provide a powerful and extensively-usable tool in theoretical physics. This homotopy algebraic approach to QFT has been mostly developed since around 2018-19, and there are few workshops focusing on this recent topic yet. We hope to provide such an opportunity, potentially facilitating new and groundbreaking threads of research.
We also provides mini-course of introductory lectures for newcomers to this topic: Lectures will cover the BV formalism, homotopy algebra, its mathematical aspects and related topics, and review the key concepts behind the recent developments.
Topics covered by the workshop are as follows.
- Homotopy algebra in classical or quantum field theory
- Batalin-Vilkovisky formalism
- Connection between BV and homotopy algebraic structure
- Homological perturbation lemma in field theory
- S-matrix and minimal model theorem
- Effective field theory and homotopy transfer
- Feynman transformation and algebra over modular operad
- Possible applications