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- W4386977804 abstract "The Kontsevich-Soibelman wall-crossing formula is known to control the jumping behavior of BPS state counting indices in four-dimensional theories with $mathcal{N}=2$ supersymmetry. The formula can take two equivalent forms: a ``fermionic'' form with nice positivity properties and a ``bosonic'' form with a clear physical interpretation. In an important class of examples, the fermionic form of the formula has a mathematical categorification involving PBW bases for a Cohomological Hall Algebra. The bosonic form lacks an analogous categorification. We construct an equivalence of chain complexes which categorifies the simplest example of the bosonic wall-crossing formula: the bosonic pentagon identity for the quantum dilogarithm. The chain complexes can be promoted to differential graded algebras which we relate to the PBW bases of the relevant CoHA by a certain quadratic duality. The equivalence of complexes then follows from the relation between quadratic duality and Koszul duality. We argue that this is a special case of a general phenomenon: the bosonic wall-crossing formulae are categorified to equivalences of $A_infty$ algebras which are quadratic dual to PBW presentations of algebras which underlie the fermionic wall-crossing formulae. We give a partial interpretation of our differential graded algebras in terms of a holomorphic-topological version of BPS webs." @default.
- W4386977804 created "2023-09-23" @default.
- W4386977804 creator A5057355170 @default.
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- W4386977804 date "2023-09-21" @default.
- W4386977804 modified "2023-10-18" @default.
- W4386977804 title "Categorical Pentagon Relations and Koszul Duality" @default.
- W4386977804 doi "https://doi.org/10.48550/arxiv.2309.12103" @default.
- W4386977804 hasPublicationYear "2023" @default.
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