Modular operads relevant to string theory can be equipped with an additional
structure, coming from the connected sum of surfaces. Motivated by this
example, we introduce a notion of connected sum for general modular operads. We
show that a connected sum induces a commutative product on the space of
functions associated to the modular operad. Moreover, we combine this product
with Barannikov’s non-commutative Batalin-Vilkovisky structure present on this
space of functions, obtaining a Beilinson-Drinfeld algebra. Finally, we study
the quantum master equation using the exponential defined using this
commutative product.
