On correspondences between toric singularities and image-webs Original Research Article

We study four-dimensional image gauge theories which arise from D3-brane probes of toric Calabi–Yau threefolds. There are some standing paradoxes in the literature regarding relations among image-webs, toric diagrams and various phases of the gauge theories, we resolve them by proposing and carefully distinguishing between two kinds of image-webs: toric and quiver image-webs. The former has a one to one correspondence with the toric diagram while the latter can correspond to multiple gauge theories. The key reason for this ambiguity is that a given quiver image-web cannot capture non-chiral matter fields in the gauge theory. To support our claim we analyse families of theories emerging from partial resolution of Abelian orbifolds using the Inverse Algorithm of as well as image-web techniques. We present complex inter-relations among these theories by higgsing, blowups and brane splittings. We also point out subtleties involved in the ordering of legs in the image diagram.