Solving the Yang-Baxter equation

Abstract: The Yang-Baxter equation is an important equation that appears in many different areas of physics. It signals the presence of integrable structures which appear in topics ranging from condensed matter physics to holography. In this talk I will discuss a new method to find all regular solutions of the Yang-Baxter equation by using the so-called boost automorphism. The main idea behind this method is to use the Hamiltonian rather than the R-matrix as a starting point. I will demonstrate our method by classifying all solutions of the Yang-Baxter equation of eight-vertex type. I will also consider certain 9x9 and 16x16 solutions and give new integrable models in all of these cases. As a further application, I will discuss all integrable deformations of R-matrices that appear in the lower-dimensional cases of the AdS/CFT correspondence.

HEP - theorymathematical physicsexactly solvable and integrable systems

Audience: researchers in the topic

London Integrability Journal Club

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