Braids, Walls, and Mirrors
arXiv:1110.2115
Abstract
We construct 3d, N=2 supersymmetric gauge theories by considering a one-parameter `R-flow' of 4d, N=2 theories, where the central charges vary while preserving their phase order. Each BPS state in 4d leads to a BPS particle in 3d, and thus each chamber of the 4d theory leads to a distinct 3d theory. Pairs of 4d chambers related by wall-crossing, R-flow to mirror pairs of 3d theories. In particular, the 2-3 wall-crossing for the A_2 Argyres-Douglas theory leads to 3d mirror symmetry for N_f=1 SQED and the XYZ model. Although our formalism applies to arbitrary N=2 models, we focus on the case where the parent 4d theory consists of pairs of M5-branes wrapping a Riemann surface, and develop a general framework for describing 3d N=2 theories engineered by wrapping pairs of M5-branes on three-manifolds. Each 4d chamber, which corresponds to a dual 3d description, maps to a particular tetrahedral decomposition of the UV 3d geometry. In the IR the physics is captured by a single recombined M5-brane which is a branched double cover of the original UV three-manifold. The braiding of branch loci and the geometry of branch sheets play a key role in encoding the physics.
142 pages, 59 figures
References in corpus (12)
- Symmetries and Strings in Field Theory and Gravity
- Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
- Three-Dimensional Gravity Revisited
- The quantum dilogarithm and representations quantum cluster varieties
- R-Twisting and 4d/2d Correspondences
- T-Branes and Monodromy
- BPS Quivers and Spectra of Complete N=2 Quantum Field Theories
- SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
- M-theory and a Topological String Duality
- Classification of abelian spin Chern-Simons theories
- The pentagon relation for the quantum dilogarithm and quantized M_{0,5}
- Chern-Simons Theory and S-duality
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