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- W4376123034 abstract "Semi-classically equivalent field theories are related by a quasi-isomorphism between their underlying $L_infty$-algebras, but such a quasi-isomorphism is not necessarily a homotopy transfer. We demonstrate that all quasi-isomorphisms can be lifted to spans of $L_infty$-algebras in which the quasi-isomorphic $L_infty$-algebras are obtained from a correspondence $L_infty$-algebra by a homotopy transfer. Our construction is very useful: homotopy transfer is computationally tractable, and physically, it amounts to integrating out fields in a Feynman diagram expansion. Spans of $L_infty$-algebras appear naturally in many contexts within physics. As examples, we first consider scalar field theory with interaction vertices blown up in different ways. We then show that (non-Abelian) T-duality can be seen as a span of $L_infty$-algebras, and we provide full details in the case of the principal chiral model. We also present the relevant span of $L_infty$-algebras for the Penrose-Ward transform in the context of self-dual Yang-Mills theory and Bogomolny monopoles." @default.
- W4376123034 created "2023-05-12" @default.
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- W4376123034 date "2023-05-09" @default.
- W4376123034 modified "2023-09-25" @default.
- W4376123034 title "Field Theory Equivalences as Spans of $L_infty$-algebras" @default.
- W4376123034 doi "https://doi.org/10.48550/arxiv.2305.05473" @default.
- W4376123034 hasPublicationYear "2023" @default.
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