A-infinity structure in string theory and the Yang-Mills equation

TL;DR

This paper explores the A-infinity algebra structure in string theory, connecting it to the Yang-Mills equation, and introduces methods to compute corrections within this framework.

Contribution

It establishes a homotopical Maurer-Cartan framework in string theory, linking A-infinity structures to Yang-Mills equations and their alpha'-corrections.

Findings

Recovered Yang-Mills equation from homotopical Maurer-Cartan equation

Identified first alpha'-correction to Yang-Mills equation

Proposed method to calculate all higher-order corrections

Abstract

We consider local operators of CFT inserted at the boundary of the worldsheet and an infinite set of maps that act on a space of the local operators. These maps have natural CFT interpretation and form A-infinity algebra. In terms of these operators we define the homotopical Maurer-Cartan equation, find its symmetries and explore its properties. Further we recover the Yang-Mills equation from the homotopical Maurer-Cartan equation, identify the first alpha'-correction to it and propose method for calculation all corrections.