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Modular operads with connected sum and Barannikov’s theory. (English) Zbl 07285966

Summary: We introduce the connected sum for modular operads. This gives us a graded commutative associative product, and together with the BV bracket and the BV Laplacian obtained from the operadic composition and self-composition, we construct the full Batalin-Vilkovisky algebra. The BV Laplacian is then used as a perturbation of the special deformation retract of formal functions to construct a minimal model and compute an effective action.

MSC:

18M60 Operads (general)
81T99 Quantum field theory; related classical field theories
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References:

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