Surface defects and resolvents

We study a large class of BPS surface defects in 4d$$ \mathcal{N}=2 $$ gauge theories. They are defined by coupling a 2d$$ \mathcal{N}=\left( {2,2} \right) $$ gauged linear sigma model to the 4d bulk degrees of freedom. Our main result is an efficient computation of the effective twisted superpotential for all these models in terms of a basic object closely related to the resolvent of the 4d gauge theory, which encodes the curve describing the …