2014/08/12 by Mikhail Kapranov, Maxim Kontsevich, Kapranov, Mikhail +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1408.2673
openalex publication_date 2014/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study algebraic structures (L_∞ and A_∞-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_∞-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.