Mitchell Institute for Fundamental Physics & Astronomy
College Station, Texas 77843
In the study of **N=2** supersymmetric theories in 4 dimensions, a very useful tool is the notion of “spectral network”, which arises when one studies BPS wall-crossing in the presence of certain sorts of line and surface defects. For 3d **N=2** theories it seems that a similar notion of “spectral network” exists, and can be used to compute IR quantities such as the vacuum structure and effective superpotentials when the theory is compactified on **S^1**. When applied to theories of “class R” introduced by Dimofte-Gaiotto-Gukov, this amounts to a new way of computing classical Chern-Simons invariants for flat connections (and this is the only case we really understand so far). I will explain some aspects of this story. This is work in progress with Dan Freed.