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.