Heterotic Surface Defects and Dualities from 2d/4d Indices

Understand

Starting with the superconformal indices for 4d N=2 and N=1 supersymmetric gauge theories, which are related by superpotential deformation, we perform the contour integrations and isolate the residue contributions which can be attributed to the surface defects.

• These defects can be interpreted as the IR limit of dynamical vortices.
• Given the 2d N=(2,2) and N=(0,2) world sheet theories for these surface defects, we then verify this statement by explicitly computing their elliptic genera and identifying their fugacity parameters through superconformal algebras.
• We show them precisely match, and the results extend previous prescriptions for inserting surface defects into 4d supersymmetric partition functions to N=1 setting.