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• W3114967326 abstract "Given a gauged linear sigma model (GLSM) $${mathcal {T}}_{X}$$ realizing a projective variety X in one of its phases, i.e. its quantum Kähler moduli has a geometric point, we propose an extended GLSM $${mathcal {T}}_{{mathcal {X}}}$$ realizing the homological projective dual category $${mathcal {C}}$$ to $$D^{b}Coh(X)$$ as the category of B-branes of the Higgs branch of one of its phases. In most of the cases, the models $${mathcal {T}}_{X}$$ and $${mathcal {T}}_{{mathcal {X}}}$$ are anomalous and the analysis of their Coulomb and mixed Coulomb-Higgs branches gives information on the semiorthogonal/Lefschetz decompositions of $${mathcal {C}}$$ and $$D^{b}Coh(X)$$ . We also study the models $${mathcal {T}}_{X_{L}}$$ and $${mathcal {T}}_{{mathcal {X}}_{L}}$$ that correspond to homological projective duality of linear sections $$X_{L}$$ of X. This explains why, in many cases, two phases of a GLSM are related by homological projective duality. We study mostly abelian examples: linear and Veronese embeddings of $${mathbb {P}}^{n}$$ and Fano complete intersections in $${mathbb {P}}^{n}$$ . In such cases, we are able to reproduce known results as well as produce some new conjectures. In addition, we comment on the construction of the HPD to a nonabelian GLSM for the Plücker embedding of the Grassmannian G(k, N)." @default.
• W3114967326 created "2021-01-05" @default.
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• W3114967326 date "2022-05-08" @default.
• W3114967326 modified "2023-09-27" @default.
• W3114967326 title "A GLSM View on Homological Projective Duality" @default.
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• W3114967326 doi "https://doi.org/10.1007/s00220-022-04401-1" @default.
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