On the uniqueness of L∞ bootstrap: Quasi-isomorphisms are Seiberg-Witten maps

In the context of the recently proposed L∞ bootstrap approach, the question arises whether the so constructed gauge theories are unique solutions of the L∞ relations. Physically, it is expected that two gauge theories should be considered equivalent if they are related by a field redefinition described by a Seiberg-Witten map. To clarify the consequences in the L∞ framework, it is proven that Seiberg-Witten maps between physically equivalent gauge theories correspond to certain relations of quasi-isomorphisms of the underlying L∞ algebras. The proof suggests an extension of the definition of a Seiberg-Witten map to the closure conditions of two gauge transformations and the dynamical equations of motion.