Modular envelopes, OSFT and nonsymmetric (non$\Sigma$) modular operads
Abstract
Our aim is to introduce and advocate non$\Sigma$ (nonsymmetric) 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2014
 arXiv:
 arXiv:1410.3414
 Bibcode:
 2014arXiv1410.3414M
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Geometric Topology;
 18D50;
 32G15;
 18D35
 EPrint:
 27 pages. Numerous references added, intrinsic definition of cyclic order used