Solving the noncommutative Batalin-Vilkovisky equation

Abstract

I show that a summation over ribbon graphs with legs gives the construction of the solutions to the noncommutative Batalin-Vilkovisky equation, including the equivariant version. This generalizes the known construction of A-infinity algebra via summation over ribbon trees. These solutions give naturally the supersymmetric matrix action functionals, which are the gl(N)-equivariantly closed differential forms on the matrix spaces, which were introduced in one of my previous papers "Noncommmutative Batalin-Vilkovisky geometry and Matrix integrals" (arXiv:0912.5484, electronic CNRS preprint hal-00102085(28/09/2006)).

17 pages, electronic CNRS preprint hal-00464794 (17/03/2010)

References in corpus (4)

• Modular operads and Batalin-Vilkovisky geometry
• Noncommmutative Batalin-Vilkovisky geometry and Matrix integrals
• Wheeled pro(p)file of Batalin-Vilkovisky formalism
• On the construction of A-infinity structures

Cited by in corpus (5)

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• Perturbative path-integral of string field and the $A_{\infty }$ structure of the BV master equation
• Lagrangian Relations and Quantum $L_{\infty }$ Algebras
• EA-Matrix integrals of associative algebras and equivariant localization