This chapter is a collection of techniques, warnings, facts and ideas that are sometimes regarded as theoretical curiosities in high-energy physics but have important consequences in condensed matter physics. In particular, we describe theories that have the property of having finite but undetermined radiative corrections that also happen to describe topological semi-metallic phases in condensed matter. In the process, we describe typical methods in high-energy physics that illustrate the working principles to describe a given phase of matter and its response to external fields.

Chapter in "Topological Matter". Springer Series in Solid-State Sciences, vol 190. Springer. Based on three lectures given at the 2017 Topological Matter School, available at https://www.youtube.com/watch?v=ZmmOe61Ea4M , https://www.youtube.com/watch?v=Gw6dmVPSI_g , and https://www.youtube.com/watch?v=UG6rwZdQabA