Non-Perturbative Schwinger-Dyson Equations for 3d ${\cal N} = 4$ Gauge Theories

The author derives and interprets non-perturbative Schwinger-Dyson identities satisfied by correlation functions of a certain gauge-invariant operator, the "vortex character," in 3d ${\cal N} = 4$ gauge theories. These identities are obtained from various physical perspectives, including the vortex quantum mechanics, the 3d gauge theory, a 2d q-Toda theory, and 6d little string theory.