## Algebraic structures of string field theory

### Martin Markl – 20 November 2013

We explain that the BRST complex of closed string field theory is an algebra over the bar construction (called in this context the Feynman transform) of the modular envelope of the operad Com for commutative associative algebras. This algebraic structure is sometimes called a loop or quantum homotopy Lie algebra.

We then discuss an analogous result for open strings. Here the central problem lies already in describing the modular envelope of the operad Ass for associative algebras. We show that this task has an interesting geometric content related to the cow's stomach.

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