Walls, Lines, and Spectral Dualities in 3d Gauge Theories

TL;DR

This paper explores spectral dualities in 3d N=2 gauge theories, analyzing BPS defects, S-duality walls, and their connections to integrable systems, knot invariants, and spectral curves, revealing new dualities and computational methods.

Contribution

It introduces a novel spectral duality between 3d gauge theories and integrable systems, extending previous dualities and applying them to knot and 3-manifold invariants.

Findings

Computed period integrals for BPS defects and walls.

Established a spectral duality linking 3d gauge theories and integrable systems.

Connected period calculations to knot invariants and domain wall spectra.

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.