Homotopy Relations for Topological VOA
  We consider a parameter-dependent version of the homotopy associative part of the Lian-Zuckerman homotopy algebra and provide the interpretation of multilinear operations of this algebra in terms of integrals over certain polytopes. We explicitly prove the pentagon relation up to homotopy and propose a construction of higher operations. 
Anton M. Zeitlin
math.QA hep-th math-ph math.MP