  We propose two kinds of gauged linear sigma models whose moduli spaces are
real eight-dimensional hyperKahler and Calabi-Yau manifolds, respectively.
Here, hyperKahler manifolds have sp(2) holonomy in general and are dual to Type
IIB (p,q)5-brane configurations. On the other hand, Calabi-Yau fourfolds are
toric varieties expressed as quotient spaces. Our model involving fourfolds is
different from the usual one which is directly related to a symplectic quotient
procedure. Remarkable features in newly-found three-dimensional
Chern-Simons-matter theories appear here as well, such as dynamical
Fayet-Iliopoulos parameters, one dualized photon and its residual discrete
gauge symmetry.
