ADE Spectral Networks and Decoupling Limits of Surface Defects

Abstract

We study vacua and BPS spectra of canonical surface defects of class $\mathcal{S}$ theories in different decoupling limits using ADE spectral networks. In some regions of the IR moduli spaces of these 2d-4d systems, the mixing between 2d and 4d BPS states is suppressed, and the spectrum of 2d-4d BPS states becomes that of a 2d $\mathcal{N}=(2,2)$ theory. For some decoupling limits, we identify the 2d theories describing the surface defects with nonlinear sigma models and coset models that have been previously studied. We also study certain cases where the decoupling limit of a surface defect exhibits a set of vacua and a BPS spectrum that appear to be entirely new. A detailed analysis of these spectra and their wall-crossing behavior is performed.

arXiv comment50 pages with figures generated using http://het-math2.physics.rutgers.edu/loom and http://het-math2.physics.rutgers.edu/cproj ; v2: version published in JHEP

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Cited by in corpus (6)

• Surface Defect Indices and 2d-4d BPS States
• Exponential BPS graphs and D brane counting on toric Calabi-Yau threefolds: Part I
• An infrared bootstrap of the Schur index with surface defects
• Index-Like Theorems from Line Defect Vevs
• Quivers, Line Defects and Framed BPS Invariants
• Les Houches lectures on non-perturbative Seiberg-Witten geometry