On the Uniqueness of L${}_{\infty }$ bootstrap: Quasi-isomorphisms are Seiberg-Witten Maps

Abstract

In the context of the recently proposed L${}_{\infty }$ bootstrap approach, the question arises whether the so constructed gauge theories are unique solutions of the L${}_{\infty }$ 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${}_{\infty }$ framework, it is proven that Seiberg-Witten maps between physically equivalent gauge theories correspond to quasi-isomorphisms of the underlying L${}_{\infty }$ 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.

22 pages, v2: references updated, statement of theorem 1 corrected