Deconstructing Defects

TL;DR

This paper develops a method to derive four-dimensional superconformal indices with surface defects from three-dimensional theories, providing new insights into defect structures and supersymmetry preservation.

Contribution

It introduces an exact-deconstruction approach to lift 3D partition functions with defects to 4D indices, including surface and Wilson-loop defects, with evidence for supersymmetry enhancements.

Findings

Derived 4D indices with surface defects from 3D theories.

Established a prescription for (4,0) supersymmetric surface defects.

Clarified computational and conceptual aspects of exact deconstruction.

Abstract

We use the exact-deconstruction prescription to lift various squashed-$S^3$ partition functions with supersymmetric-defect insertions to four-dimensional superconformal indices. Starting from three-dimensional circular-quiver theories with vortex-loop-operator insertions, we recover the index of four-dimensional theories in the presence of codimension-two surface defects with (2,2) supersymmetry. The case of deconstruction with Wilson-loop insertions is discussed separately. We provide evidence that a certain prescription leads to the index of four-dimensional theories in the presence of surface defects with (4,0) supersymmetry. In addition, we deconstruct the index of four-dimensional gauge theories with codimension-one 1/2-BPS defects, starting from three-dimensional circular-quiver theories containing localised matter/gauge-field insertions at specific nodes. We also clarify certain calculational and conceptual points related to exact deconstruction.