2-Morse Theory and the Algebra of the Infrared

Soukhanov, Lev

doi:10.48550/arxiv.1810.08776

Cited by 2 publications

(3 citation statements)

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“…Our aim is to look at this problem in a perspective of the algebra of the infrared discovered in [12] and developed its mathematical counterpart in [13] (see also [14][15][16]). A common proposal for physical categorification of various quantities indicates that such geometric objects as cohomology appear in consideration of topologically protected Hilbert subspaces of quantum theories with supersymmetry [17].…”

Section: Supersymmetric Interfacesmentioning

confidence: 99%

“…Rather we could perform perturbative expansion in a regime ∆µ/ √ r 1 confirming each soliton solution (4. 16) is accompanied by a single solution to the complete system. The resulting expressions turn out to be rather bulky and we will never use their explicit form, therefore we omit them in our consideration.…”

Section: Jhep10(2022)076mentioning

confidence: 99%

“…(5.28) 16 Here notation (3.65) and concatenation rule (3.66) are naturally extended to include simple boundary condition choices. So that L corresponding to a specific vacuum choice are allowed to terminate a "string" of quasi-particle letters Xij.…”

Section: Categorical Parallel Transportmentioning

confidence: 99%

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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.

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Section: Supersymmetric Interfacesmentioning

confidence: 99%

Section: Jhep10(2022)076mentioning

confidence: 99%

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

Galakhov

2022

J. High Energ. Phys.

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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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2-Morse Theory and the Algebra of the Infrared

Cited by 2 publications

References 0 publications

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

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

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