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SUMMARY:On Supersymmetric Interface Defects\, Brane Parallel Transport and
Higgs-Coulomb Duality
DTSTART;VALUE=DATE-TIME:20210531T100000Z
DTEND;VALUE=DATE-TIME:20210531T111500Z
DTSTAMP;VALUE=DATE-TIME:20230323T180714Z
UID:indico-contribution-5712@indico.ipmu.jp
DESCRIPTION:Speakers: Dimitrii Galakhov (Kavli IPMU\, U. Tokyo)\nWe concen
trate 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) theo
ries. We consider these examples of QFTs in the SchrÃ¶dinger picture and i
dentify Hilbert spaces of BPS states with morphisms in triangulated Abelia
n categories of D-brane boundary conditions. As a result of Higgs-Coulomb
duality D-brane categories on IR vacuum moduli spaces are equivalent\, thi
s resembles an analog of homological mirror symmetry. Following constructi
on ideas behind the Gaiotto-Moore-Witten algebra of the infrared one is ab
le to introduce interface defects in these theories and associate them to
D-brane parallel transport functors. We concentrate on surveying simple ex
amples\, analytic when possible calculations\, numerical estimates and sim
ple physical picture behind curtains of geometric objects. Categorificatio
n of hypergeometric series analytic continuation is derived as an Atiyah f
lop of the conifold. Finally we arrive to an interpretation of the braid g
roup action on the derived category of coherent sheaves on cotangent bundl
es to flag varieties as a categorification of Berry connection on the Faye
t-Illiopolous parameter space of a sigma-model with a quiver variety targe
t space. The talk is based on arXiv:2105.07602\n\nhttps://indico.ipmu.jp/e
vent/387/contributions/5712/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5712/
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