Speaker
Description
The presence of integrability in a model provides us with powerful tools to solve it. It plays a role in several different areas of physics, being in particular responsible for remarkable progress in the context of AdS/CFT. To ask whether a model is integrable is therefore a very relevant question, but not always an easy one. In this talk, I will discuss two methods to construct new integrable models. The first allows to classify integrable models whose Hamiltonians have nearest-neighbor interaction, while the second can also be applied to long-range spin chains. Examples will include new integrable deformations of $AdS_2$ and $AdS_3$ S-matrices; and the Lax operator and R-matrix of the two-loop $SU(2)$ sector in $\mathcal{N}=4$ SYM. I will also show that all known range 3 integrable deformations of the 6-vertex model are generated by an R-matrix. This talk will be mostly based on arxiv:2109.00017 and arxiv:2206.08390.
