Noncommutative Batalin-Vilkovisky geometry and matrix integrals

Serguei Barannikov

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

I study the new type of supersymmetric matrix models associated with any solution to the quantum master equation of the noncommutative Batalin-Vilkovisky geometry. The asymptotic expansion of the 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 Bernstein-Leites 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 matrix integrals in the case of dimension zero is a supersymmetric extension of the Kontsevich model of 2-dimensional gravity.

Original languageEnglish
Pages (from-to)359-362
Number of pages4
JournalComptes Rendus Mathematique
Volume348
Issue number7-8
DOIs
Publication statusPublished - Apr 2010
Externally publishedYes

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