Topological Field Theories from and for 4d SUSY Gauge Theories

AGT-correspondences give profound relations between certain families of $\mathcal{N}=2$ supersymmetric gauge theories in four dimensions and conformal field theories in two dimensions. Subsequent investigations of the AGT-correspondences revealed a new type of topological field theory associated to these theories that captures completely the dependence of important physical quantities on the gauge coupling constants, including perturbative and non-perturbative corrections. The topological field theories and chiral data associated to $\mathcal{N}=2$ supersymmetric field theories are the central objects of study in this project. We present first steps towards a precise mathematical framework for them in which loop and surface operators play a particularly important role