A-infinity structure in string theory and the Yang-Mills equation
  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. 
Dmitry Grigoryev, Pavel Khromov
hep-th