157 research outputs found
Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields
We construct a generalization of the variations of Hodge structures on
Calabi-Yau manifolds. It gives a Mirror partner for the theory of genus=0
Gromov-Witten invariantsComment: 12 pages, AMS-TeX; typos and a sign corrected, appendix added.
Submitted to IMR
Solving the noncommutative Batalin-Vilkovisky equation
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)).Comment: 17 pages, electronic CNRS preprint hal-00464794 (17/03/2010
Symmetries of WDVV equations
We say that a function F(tau) obeys WDVV equations, if for a given invertible
symmetric matrix eta^{alpha beta} and all tau \in T \subset R^n, the
expressions c^{alpha}_{beta gamma}(tau) = eta^{alpha lambda} c_{lambda beta
gamma}(tau) = eta^{alpha lambda} \partial_{lambda} \partial_{beta}
\partial_{gamma} F can be considered as structure constants of commutative
associative algebra; the matrix eta_{alpha beta} inverse to \eta^{\alpha \beta}
determines an invariant scalar product on this algebra. A function x^{alpha}(z,
tau) obeying \partial_{alpha} \partial_{beta} x^{gamma} (z, tau) = z^{-1}
c^{varepsilon}_{alpha beta} \partial_{epsilon} x^{gamma} (z, tau) is called a
calibration of a solution of WDVV equations. We show that there exists an
infinite-dimensional group acting on the space of calibrated solutions of WDVV
equations (in different form such a group was constructed in [2]). We describe
the action of Lie algebra of this group.Comment: LaTeX, 15 page
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