| Abstract |
I will discuss the sine–Gordon QFT, which lies in the same universality class as the Coulomb gas and the XY model, and exhibits the BKT phase transition (Nobel prize 2016). The sine–Gordon action admits infinitely many homotopy classes. Even though the action has no energy minimizers in homotopy classes with high topological charge, I will show that the Gibbs measure nevertheless concentrates and exhibits Ornstein–Uhlenbeck fluctuations around the multi-soliton manifold. I will then discuss the geometry of this multi-soliton manifold, including how solitons are arranged, such as their expected locations and gaps. Furthermore, I will explain the asymptotics of the partition function using Gaussian multiplicative chaos.
Based on joint work with Hao Shen and Philippe Sosoe.
https://arxiv.org/abs/2512.23957 |
