Solving the Noncommutative Batalin-Vilkovisky Equation

Serguei Barannikov

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Given an odd symmetry acting on an associative algebra, I show that the summation over arbitrary ribbon graphs gives the construction of the solutions to the noncommutative Batalin-Vilkovisky equation, introduced in (Barannikov in IMRN, rnm075, 2007), and to the equivariant version of this equation. This generalizes the known construction of A-algebra via summation over ribbon trees. I give also the generalizations to other types of algebras and graph complexes, including the stable ribbon graph complex. These solutions to the noncommutative Batalin-Vilkovisky equation and to its equivariant counterpart, provide naturally the supersymmetric matrix action functionals, which are the gl(N)-equivariantly closed differential forms on the matrix spaces, as in (Barannikov in Comptes Rendus Mathematique vol 348, pp. 359-362.

Original languageEnglish
Pages (from-to)605-628
Number of pages24
JournalLetters in Mathematical Physics
Issue number6
Publication statusPublished - Jun 2013
Externally publishedYes


  • A-algebras
  • B-model
  • Batalin-Vilkovisky formalism
  • cyclic homology
  • Feynman diagrams
  • matrix integrals
  • mirror symmetry
  • noncommutative algebraic geometry
  • ribbon graphs


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