The virtue of defects in 4D gauge theories and 2D CFTs

We advance a correspondence between the topological defect operators in Liouville and Toda conformal field theories — which we construct — and loop operators and domain wall operators in four dimensional $$ \mathcal{N} = 2 $$ supersymmetric gauge theories on S4. Our computation of the correlation functions in Liouville/Toda theory in the presence of topological defect operators, which are supported on curves on the Riemann surface, yields the …