Serre duality for Khovanov-Rozansky homology

Gorsky, Eugene; Hogancamp, Matthew; Mellit, Anton; Nakagane, Keita

doi:10.48550/arxiv.1902.08281

Cited by 3 publications

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“…up to a regrading (see Corollary 1.12 in [GHMN19]. Since we compute HH(X m,n ) only as a complex of Z-modules, we are unable to make computations for negative torus links.…”

Section: Introductionmentioning

confidence: 99%

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Torus link homology

Hogancamp¹,

Mellit²

2019

Preprint

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“…up to a regrading (see Corollary 1.12 in [GHMN19]. Since we compute HH(X m,n ) only as a complex of Z-modules, we are unable to make computations for negative torus links.…”

Section: Introductionmentioning

confidence: 99%

“…Note also that in degree zero, Hochschild cohomology is just HH 0 := Hom R⊗R (R, −). The torus link T (m, n) is also the closure of the braid β m,n := (σ 1 • • • σ m−1 ) n , and the full twist braid is FT m := β m,m acts as a sort of Serre functor (Theorem 1.1 in [GHMN19]), from which it follows that…”

Section: Introductionmentioning

confidence: 99%

Torus link homology

Hogancamp¹,

Mellit²

2019

Preprint

Self Cite

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“…A categorification of Chern-Simons link invariants [74,75] opened a vast amount of opportunities for applications in both string theories [76][77][78][79][80][81][82][83][84][85][86] and pure mathematics [87][88][89][90][91][92] as well as their profound synthesis to discover underlying structures in relations between physics and geometry. Unfortunately, we are unable to cover literature for this popular topic even partially and indicate just few sources the reader could use to find a particular subject interesting for a concrete application.…”

Section: Braid Group Categorification Affine Grassmannians Crystal Me...mentioning

confidence: 99%

On supersymmetric interface defects, brane parallel transport, order-disorder transition and homological mirror symmetry

Galakhov

2022

J. High Energ. Phys.

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We concentrate on a treatment of a Higgs-Coulomb duality as an absence of manifest phase transition between ordered and disordered phases of 2d $$ \mathcal{N} $$ N = (2, 2) theories. We consider these examples of QFTs in the Schrödinger picture and identify Hilbert spaces of BPS states with morphisms in triangulated categories of D-brane boundary conditions. As a result of Higgs-Coulomb duality D-brane categories on IR vacuum moduli spaces are equivalent, this resembles an analog of homological mirror symmetry. Following construction ideas behind the Gaiotto-Moore-Witten algebra of the infrared one is able to introduce interface defects in these theories and associate them to D-brane parallel transport functors. We concentrate on surveying simple examples, analytic when possible calculations, numerical estimates and simple physical picture behind curtains of geometric objects. Categorification of hypergeometric series analytic continuation is derived as an Atiyah flop of the conifold. Finally we arrive to an interpretation of the braid group action on the derived category of coherent sheaves on cotangent bundles to flag varieties as a categorification of Berry connection on the Fayet-Illiopolous parameter space of a sigma-model with a quiver variety target space.

show abstract

“…A categorification of Chern-Simons link invariants [68,69] opened a vast amount of opportunities for applications in both string theories [70][71][72][73][74][75][76][77][78][79] and pure mathematics [80][81][82][83][84][85] as well as their profound synthesis to discover underlying structures in relations between physics and geometry. Unfortunately, we are unable to cover literature for this popular topic even partially and indicate just few sources the reader could use to find a particular subject interesting for a concrete application.…”

Section: Atiyah Flop and Hypergeometric Seriesmentioning

confidence: 99%

On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry

Galakhov¹

2021

Preprint

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We concentrate on a treatment of a Higgs-Coulomb duality as an absence of manifest phase transition between ordered and disordered phases of 2d N = (2, 2) theories. We consider these examples of QFTs in the Schrödinger picture and identify Hilbert spaces of BPS states with morphisms in triangulated Abelian categories of D-brane boundary conditions. As a result of Higgs-Coulomb duality D-brane categories on IR vacuum moduli spaces are equivalent, this resembles an analog of homological mirror symmetry. Following construction ideas behind the Gaiotto-Moore-Witten algebra of the infrared one is able to introduce interface defects in these theories and associate them to D-brane parallel transport functors. We concentrate on surveying simple examples, analytic when possible calculations, numerical estimates and simple physical picture behind curtains of geometric objects. Categorification of hypergeometric series analytic continuation is derived as an Atiyah flop of the conifold. Finally we arrive to an interpretation of the braid group action on the derived category of coherent sheaves on cotangent bundles to flag varieties as a categorification of Berry connection on the Fayet-Illiopolous parameter space of a sigma-model with a quiver variety target space.

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Serre duality for Khovanov-Rozansky homology

Cited by 3 publications

References 0 publications

Torus link homology

Torus link homology

On supersymmetric interface defects, brane parallel transport, order-disorder transition and homological mirror symmetry

On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry

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