Surface defects and instanton-vortex interaction

We propose a simple formula for the 4d-2d partition function of half-BPS surface defects in d=4, N=2 gauge theories: Z4d-2d=〈Z2d〉4d. Our results are applicable for any surface defect obtained by gauging a 2d flavor symmetry using a 4d gauge group. For defects obtained via the Higgsing procedure, our formula reproduces the recent calculation by Pan and Peelaers. For Gukov-Witten defects our results reproduce the orbifold calculation by Kanno and Tachikawa. We emphasize the role of “negative vortices” which are realized as negative D0 branes.