On the Uniqueness of L$_\infty$ bootstrap: Quasi-isomorphisms are Seiberg-Witten Maps
| Autor: | Vladislav G. Kupriyanov, Ralph Blumenhagen, Matthias Traube, Max Brinkmann |
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| Rok vydání: | 2018 |
| Předmět: |
High Energy Physics - Theory
Pure mathematics 010308 nuclear & particles physics Homotopy Closure (topology) FOS: Physical sciences Statistical and Nonlinear Physics Field (mathematics) Context (language use) Mathematical Physics (math-ph) Gauge (firearms) 01 natural sciences High Energy Physics::Theory High Energy Physics - Theory (hep-th) 0103 physical sciences Gauge theory Uniqueness 010306 general physics Equations for a falling body Mathematics::Symplectic Geometry Mathematical Physics Mathematics |
| DOI: | 10.48550/arxiv.1806.10314 |
| Popis: | 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. Comment: 22 pages, v2: references updated, statement of theorem 1 corrected |
| Databáze: | OpenAIRE |
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