Line Defects in Three Dimensional Mirror Symmetry beyond Linear Quivers

The map of half-BPS line defects under mirror symmetry has previously been worked out for 3d $\mathcal{N}=4$ linear quivers with unitary gauge groups, where these defects have a clear realization in terms of a brane picture in Type IIB String Theory. In this work, we initiate the study of line defects and the associated mirror maps for more general 3d $\mathcal{N}=4$ quiver gauge theories from a QFT approach, using the $S$-type operations introduced in \cite{Dey:2020hfe}. In particular, our construction does not rely on any String Theory realization of the quiver gauge theories and the defects. After discussing the general framework for the construction of these line defects and their mirror maps, we focus on quiver gauge theories of the $D$-type and the affine $D$-type with unitary gauge groups, as a concrete set of examples. Some of the line defects we study admit a Hanany-Witten description and we show that the associated mirror maps predicted by the Type IIB construction in these cases agree with the QFT computation. In addition, we study an example involving defects in an affine $D$-type theory, for which the dual theory is not directly realized by the Type IIB description. In a companion paper, we will discuss defects in infinite families of non-ADE quivers using the general construction developed in this paper.