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

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##### Citation

Blumenhagen, R., Brinkmann, M., Kupriyanov, V., & Traube, M. (2018). On the Uniqueness
of L$_\infty$ bootstrap: Quasi-isomorphisms are Seiberg-Witten Maps.* Journal of Mathematical Physics,*
(59), 123505. Retrieved from https://publications.mppmu.mpg.de/?action=search&mpi=MPP-2018-146.

Cite as: https://hdl.handle.net/21.11116/0000-0003-F873-4

##### 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.