Title: Constructing new solutions of the Yang-Baxter equation

Abstract: Some theories have, in addition to momentum and energy, higher conserved charges. These theories are said to be integrable and can be exactly solved. Examples are the Kepler problem, Hubbard model and various versions of the  AdS/CFT correspondence. The main ingredient of an integrable theory is an object called the R-matrix which satisfies the so-called Yang-Baxter equation. In this talk, after a brief review of integrable models, I will introduce a new method to find solutions of the Yang-Baxter equation, using the so-called boost operator, and use it to classify R-matrices in various set-ups. Using this method we were able to find new interesting integrable models. We also constructed an integrable deformation of a Hubbard-like model and deformations of R-matrices from the AdS/CFT correspondence as I will show in this talk.

Talk – Video

Talk – Slides