Deconstructing Defects

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.

arXiv comment46 pages, 9 figures; v2: interpretational aspects of the deconstructed indices clarified and discussion on codimension-one defects improved; published version

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• A slow review of the AGT correspondence
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• Type-B Anomaly Matching and the 6D (2,0) Theory
• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$