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Published May 2014 | Published
Journal Article Open

Walls, lines, and spectral dualities in 3d gauge theories

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.

Additional Information

Open Access © The Authors. Article funded by SCOAP3. Received: February 15, 2014 Accepted: April 12, 2014 Published: May 12, 2014. We thank C. Beem, A. Bytsko, T. Dimofte, A. Gorsky, S. Nawata, N. Nekrasov, S. Shatashvili, P. Su lkowski, R. van der Veen for useful discussions on related topics. The work of A.G. is supported in part by the John A. McCone fellowship and by DOE Grant DE-FG02-92-ER40701. The work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02 and in part by NSF Grant PHY-0757647. The work of P.P. is supported in part by the Sherman Fairchild scholarship and by NSF Grant PHY-1050729. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.

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