Speaker
Description
Homotopy algebras provide a universal algebraic framework for constructing correlation functions in quantum field theory. Motivated by the study of open–closed duality from the perspective of string field theory, we aim to incorporate the 1/N expansion into this framework. As a first step, we propose an algebraic formula for perturbative correlation functions in the large-N limit of a zero-dimensional matrix model. In this framework, perturbative correlation functions are constructed algebraically using operators that encode the kinetic term, interactions, and Wick contractions. Rather than computing correlation functions at finite N and subsequently taking their large-N limit, we implement the large-N limit directly at the operator level. This is achieved by modifying the operator responsible for Wick contractions, without changing the operators encoding the kinetic and interaction terms. We demonstrate our formula through explicit calculations in free and interacting theories. Furthermore, we show that the resulting multi-trace correlation functions satisfy the large-N Schwinger–Dyson equations and that large-N factorization follows from the algebraic structure of the formula.