The BPS Spectrum Generator In 2d-4d Systems

Abstract

We apply the techniques provided by the recent works Gaiotto, Moore and Neitzke, to derive the most general spectrum generating functions for coupled 2d-4d $A_1$ theories of class $\mathcal{S}$, in presence of surface and line defects. As an application of the result, some well-known BPS spectra are reproduced. Our results apply to a large class of coupled 2d-4d systems, the corresponding spectrum generating functions can be easily derived from our general expressions.

38 pages; v2: references added; v3: references added, added introductory material in sections 1, 2.1, 2.2, 2.3

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• Surface Defects and Resolvents
• Spectral Networks with Spin
• A slow review of the AGT correspondence
• Surface Defect Indices and 2d-4d BPS States
• Spectral Networks and Snakes
• Spinning Particle Dynamics and ISCO in Covariant Loop Quantum Gravity
• ADE Spectral Networks and Decoupling Limits of Surface Defects
• An infrared bootstrap of the Schur index with surface defects
• Singularity Structure of N=2 Supersymmetric Yang-Mills Theories: A Review