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Speculations on higher Fukaya categories

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arxiv 2503.20906 v1 pith:3KC3VFOY submitted 2025-03-26 math.SG math.AG

James Pascaleff , Nicolò Sibilla This is my paper · ORCID
classification math.SGmath.AG
keywords shiftedcategoriesfukayahigherstacksymplecticassociatedcases
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abstract

We investigate a possible theory of higher Fukaya categories associated to $n$-shifted symplectic stacks, where $n \geq 0$. We consider two paradigmatic cases, the shifted cotangent stack of a smooth manifold and the coadjoint stack of a compact Lie group, drawing connections to the work of Teleman and 3D mirror symmetry. Our evidence includes some new results in $1$-shifted symplectic geometry.

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  1. Mirror symmetry in 3d in 3d mirror symmetry

    hep-th 2026-07 reject novelty 5.0 of 10

    For a CY3 Y, the paper sketches a 3d SYZ relation between the universal intermediate Jacobians X and X^!, but the key brane-category matchings are built into the definitions.

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