A refined 3D index is defined by adding flavor symmetry gradings to the superconformal index of T[M], yielding an explicit infinite-sum formula from Dehn surgery that is claimed to be a strictly stronger invariant than the standard 3D index.
Walls, Lines, and Spectral Dualities in 3d Gauge Theories
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abstract
In this paper we analyze various half-BPS defects in a general three dimensional N=2 supersymmetric gauge theory T. They correspond to closed paths in SUSY parameter space and their tension is computed by evaluating period integrals along these paths. In addition to such defects, we also study wall defects that interpolate between T and its SL(2,Z) transform by coupling the 3d theory to a 4d theory with S-duality wall. We propose a novel spectral duality between 3d gauge theories and integrable systems. This duality complements a similar duality discovered by Nekrasov and Shatashvili. As another application, for 3d N=2 theories associated with knots and 3-manifolds we compute periods of (super) A-polynomial curves and relate the results with the spectrum of domain walls and line operators.
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High-temperature limits on higher sheets of the superconformal index for (A1,A2n) Argyres-Douglas theories yield Gang-Kim-Stubbs 3d N=2 theories whose boundaries support Virasoro minimal model VOAs M(2,2n+3) and associated MTCs.
Wilson line defect half-indices for 3d N=2 theories with confining boundaries are exactly Askey-Wilson type moments, obtained via dual vortex defects and effective spin shifts in the index computation.
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Refined 3D index
A refined 3D index is defined by adding flavor symmetry gradings to the superconformal index of T[M], yielding an explicit infinite-sum formula from Dehn surgery that is claimed to be a strictly stronger invariant than the standard 3D index.
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Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
High-temperature limits on higher sheets of the superconformal index for (A1,A2n) Argyres-Douglas theories yield Gang-Kim-Stubbs 3d N=2 theories whose boundaries support Virasoro minimal model VOAs M(2,2n+3) and associated MTCs.
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Boundary lines and Askey-Wilson type moments
Wilson line defect half-indices for 3d N=2 theories with confining boundaries are exactly Askey-Wilson type moments, obtained via dual vortex defects and effective spin shifts in the index computation.