Journal of Noncommutative Geometry

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Volume 10, Issue 2, 2016, pp. 775–809
DOI: 10.4171/JNCG/248

Modular envelopes, OSFT and nonsymmetric (non-$\Sigma$) modular operads

Martin Markl[1]

(1) Czech Academy of Sciences, Prague, Czech Republic

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 rĂ´le in open string field theory. We also sketch further perspectives of the presented approach.

Keywords: Open string, surface, modular completion, terminal object

Markl Martin: Modular envelopes, OSFT and nonsymmetric (non-$\Sigma$) modular operads. J. Noncommut. Geom. 10 (2016), 775-809. doi: 10.4171/JNCG/248