2023/09/14 by Banerjee, Sibasish, Longhi, Pietro, Romo, Mauricio · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Representation Theory (math.RT) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2309.07748
A certain class of A-branes in mirrors of toric Calabi-Yau threefolds can be described through the framework of foliations. This allows to develop an explicit description of their moduli spaces based on a cell decomposition, with strata of various dimensions glued together in a way that is dictated by partial degenerations of the underlying special Lagrangian. Examples of A-branes associated with `wild' BPS states are considered in detail. The torus fixed points in their moduli spaces provide a decomposition of m-herds spectral networks into a number |Ω| of basic connected objects, where Ω is the the corresponding rank-zero Donaldson-Thomas (DT) invariant. A relation between the surgery parameters of the special Lagrangian and the baryonic semi-invariants of the representation theory of m-Kronecker quivers is also discussed, providing a local map between moduli spaces of branes related by homological mirror symmetry.