Noncommmutative Batalin-Vilkovisky geometry and Matrix integrals

Serguei Barannikov (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

I study the new type of supersymmetric equivariant matrix models associated with any solution to the quantum master equation of the noncommutative Batalin-Vilkovisky geometry. The asymptotic expansion of my matrix integrals gives homology classes in the Kontsevich compactification of the moduli spaces, which I associated with the solutions to the quantum master equation in my previous paper. I associate with the queer matrix superalgebra equipped with an odd differentiation, whose square is nonzero, the family of cohomology classes of the compactification. This family is the generating function for the products of the tautological classes. The simplest example of my A-infinity equivariant matrix integrals in the case of dimension zero is a supersymmetric extenstion of the Kontsevich model of 2-dimensional gravity.

Domaines: Géométrie algébrique [math.AG]

Serguei Barannikov. Noncommmutative Batalin-Vilkovisky geometry and Matrix integrals. Comptes Rendus. Mathématique, 2006, 2010, pp.doi: 10.1016/j.crma.2010.02.002. ⟨10.1016/j.crma.2010.02.002⟩. ⟨hal-00102085v2⟩