Perturbative correlation functions from homotopy algebras

When actions are written in terms of homotopy algebras such as A_infinity algebras and L_infinity algebras, expressions of on-shell scattering amplitudes in perturbation theory are universal for both string field theories and ordinary field theories. We thus expect that homotopy algebras can be useful in gaining insights into quantum aspects of string field theories from ordinary field theories. In addition to on-shell scattering amplitudes we find that correlation functions can also be described in terms of homotopy algebras, and in this talk we explain explicit expressions for correlation functions of scalar field theories using quantum A_infinity algebras presented in arXiv:2203.05366 and arXiv:2305.11634.



Nonperturbative correlation functions from homotopy algebras

The formula for correlation functions based on quantum A_infinity algebras in arXiv:2203.05366 and arXiv:2305.11634 requires dividing the action into the free part and the interaction part. We present a new form of the formula which does not involve such division. The new formula requires choosing a solution to the equation of motion which does not have to be real, and we claim that the formula gives correlation functions evaluated on the Lefschetz thimble associated with the solution we chose. Our formula correctly reproduces results in perturbation theory, but it can be valid nonperturbatively, and we present numerical evidence in scalar field theories in zero dimensions both in the Euclidean case and the Lorentzian case that correlation functions for a finite coupling constant can be reproduced. This talk is based on collaboration with Keisuke Konosu.