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arXiv · 2210.06517

Connected sum for modular operads and Beilinson-Drinfeld algebras

Martin Doubek·Branislav Jurčo·Lada Peksová·Ján Pulmann
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Abstract

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.

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Martin Doubek, Branislav Jurčo, Lada Peksová, Ján Pulmann. 2022-10-12. Connected sum for modular operads and Beilinson-Drinfeld algebras. https://arxiv.org/abs/2210.06517

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