The uncanny valley of finite-temperature QFT

One seemingly innocuous assumption made in introductory courses on quantum field theory is that many of the results introduced there hold only at zero temperature. While this is good enough for a lot of applications in high energy theory, many things we are interested in — such as condensed matter systems or, as far as we know, our universe — do possess a finite temperature. The aim of this talk is to give an overview of what happens when we “heat up” a QFT, mostly (but not entirely) in a perturbative setting. After a brief introduction, I will start by outlining a few different techniques suited to tackle the problem and the way they relate to each other, and show how these different structures are analogous to some that appear in the study of black holes. I will then build on these to analyse some unusual features of thermal theories, such as the loss of Lorentz invariance and the breakdown of perturbation theory as we usually intend it. To conclude, I will mention a few recent results — some coming from my own research — as for why these somewhat annoying oddities are in fact an invaluable resource to unlock new physics, or to uncover the connection between the microscopic and the macroscopic world.