On higher order Leibniz identities in TCFT

Abstract

We extend the algebra of local observables in topological conformal field theories by nonlocal operators. This allows to construct parameter-dependent operations realized via certain integrals over the compactified moduli spaces, satisfying analogues of the Leibniz and higher order Leibniz identities holding up to homotopy. We conjecture that one can construct a complete set of such operations which lead to a parameter-dependent version of Loday's homotopy Leibniz algebras.