2020/05/29 by Smirnov, Andrey, Zhou, Zijun
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2006.00118
Following the idea of Aganagic--Okounkov \citeAOelliptic, we study vertex functions for hypertoric varieties, defined by K-theoretic counting of quasimaps from ℙ1. We prove the 3d mirror symmetry statement that the two sets of q-difference equations of a 3d hypertoric mirror pairs are equivalent to each other, with Kähler and equivariant parameters exchanged, and the opposite choice of polarization. Vertex functions of a 3d mirror pair, as solutions to the q-difference equations, satisfying particular asymptotic conditions, are related by the elliptic stable envelopes. Various notions of quantum K-theory for hypertoric varieties are also discussed.