AGT and elliptic higgsed networks

In this thesis we want to introduce a current work in progress where elliptically deformed networks of DIM algebra intertwiners are used to obtain the partition function of 4d quiver gauge theories. To achieve this we start by introducing the relevant background of the AGT correspondence whose higher dimensional extension has the DIM algebra as its symmetry. The first part then gives a review of the AGT relation as well as its higher dimensional extensions to 5 and 6d. Then part two begins with a brief of DIM algebra and how its itertwiners are used to build the Higgsed networks whose matrix elements give the partition function of 3d quiver gauge theories. Finally, we deform the algebra and use the deformed networks to obtain the 4d uplift of the 3d theories.