Publication at Faculty of Mathematics and Physics |
2016
Abstract
Our aim is to introduce and advocate non-Sigma (non-symmetric) modular operads. While ordinary modular operads were inspired by the structure of the moduli space of stable complex curves, non-Sigma modular operads model surfaces with open strings outputs.
An immediate application of our theory is a short proof that the modular envelope of the associative operad is the linearization of the terminal operad in the category of non-Sigma modular operads. This gives a succinct description of this object that plays an important role in open string field theory.
We also sketch further perspectives of the presented approach.