Open-open duality with spacetime dependence

摘要: In a talk in 2010 [1] Gopakumar suggested that there might exist dualities between field theories which correspond to graph dualities of their Feynman diagrams. He called this open-open duality, in contrast to open-closed string duality. As an example he gave the two different matrix models for 2d topological gravity: the double-scaled Hermitian matrix model, where observables appear as vertices, and the Kontsevich matrix model, where observables are associated to the faces of the graph expansion.This open-open duality was demonstrated for complex matrix models in [2]. In this note we consider the extension of this open-open duality from matrix models to free field theories. In fact it had already been studied by Kazakov in 2000 [3]. The resulting dual theory is strange, in that its fields are bilocal. Considered on a discrete spacetime, it is not dissimilar to the IKKT IIB matrix model [4].