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- W1601574257 abstract "We study algebraic structures ($L_infty$ and $A_infty$-algebras) introduced by Gaiotto, Moore and Witten in their recent work devoted to certain supersymmetric 2-dimensional massive field theories. We show that such structures can be systematically produced in any number of dimensions by using the geometry of secondary polytopes, esp. their factorization properties. In particular, in 2 dimensions, we produce, out of a polyhedral coefficient system, a dg-category $R$ with a semi-orthogonal decomposition and an $L_infty$-algebra $mathfrak g$. We show that $mathfrak g$ is quasi-isomorphic to the ordered Hochschild complex of $R$, governing deformations preserving the semi-orthogonal decomposition. This allows us to give a more precise mathematical formulation of the (conjectural) alternative description of the Fukaya-Seidel category of a Kahler manifold endowed with a holomorphic Morse function." @default.
- W1601574257 created "2016-06-24" @default.
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- W1601574257 date "2014-08-12" @default.
- W1601574257 modified "2023-09-26" @default.
- W1601574257 title "Algebra of the infrared and secondary polytopes" @default.
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- W1601574257 doi "https://doi.org/10.48550/arxiv.1408.2673" @default.
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