Solving the noncommutative Batalin-Vilkovisky equation
Quantum Algebra
2014-02-04 v2 Algebraic Geometry
Symplectic Geometry
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)).
Cite
@article{arxiv.1004.2253,
title = {Solving the noncommutative Batalin-Vilkovisky equation},
author = {Serguei Barannikov},
journal= {arXiv preprint arXiv:1004.2253},
year = {2014}
}
Comments
17 pages, electronic CNRS preprint hal-00464794 (17/03/2010)