Magnetism and superconductivity in mixed-dimensional periodic Anderson model for UTe$_{2}$

UTe$_{2}$ is a strong candidate for a topological spin-triplet superconductor, and it is considered that the interplay of magnetic fluctuation and superconductivity is essential for the origin of the superconductivity. Despite various experiments suggesting ferromagnetic criticality, neutron scattering measurements observed only antiferromagnetic fluctuation and called for theories of spin-triplet superconductivity near the antiferromagnetic quantum critical point. We construct a periodic Anderson model with one-dimensional conduction electrons and two- or three-dimensional $f$-electrons, reminiscent of the band structure of UTe$_2$, and show that ferromagnetic and antiferromagnetic fluctuations are reproduced depending on the Fermi surface of $f$ electrons. These magnetic fluctuations cooperatively stabilize spin-triplet $p$-wave superconductivity. We also study hybridization dependence as a possible origin of pressure-induced superconducting phases and find that moderately large hybridization drastically changes the antiferromagnetic wave vector and stabilizes $d$-wave superconductivity.