5 papers
Quivers and BPS states in 3d and 4d
Piotr Kucharski, Pietro Longhi, Dmitry Noshchenko +2
We propose a symmetrization relation between BPS quivers encoding 4d theories and symmetric quivers associated to 3d theories. We analyse in detail…
Open strings on knot complements
Sachin Chauhan, Tobias Ekholm, Pietro Longhi
Using skein valued holomorphic curve counting techniques, we give a flow loop formula for the skein valued partition function of the Lagrangian knot complement of a fibered knot (o…
Skein traces from curve counting
Tobias Ekholm, Pietro Longhi, Sunghyuk Park +1
Given a 3-manifold , and a branched cover arising from the projection of a Lagrangian 3-manifold in the cotangent bundle of to the zero-section, we define a map from the…
The skein valued mirror of the topological vertex
Tobias Ekholm, Pietro Longhi, Vivek Shende
We count holomorphic curves in complex 3-space with boundaries on three special Lagrangian solid tori. The count is valued in the HOMFLYPT skein module of the union of the tori. Us…
The worldsheet skein D-module and basic curves on Lagrangian fillings of the Hopf link conormal
Tobias Ekholm, Pietro Longhi, Lukas Nakamura
HOMFLYPT polynomials of knots in the 3-sphere in symmetric representations satisfy recursion relations. Their geometric origin is holomorphic curves at infinity on knot conormals t…