Perturbative long-range integrable spin chains

by Ana Retore (Durham)

Thursday 9 Mar 2023, 13:30 → 14:30 Europe/Copenhagen

Aud A

There will be a student session at 13:10 before the main talk.

Abstract: The presence of integrability in planar N=4 Super Yang-Mills (SYM) was responsible for remarkable progress in our understanding of the AdS/CFT correspondence and allowed us to perform computations that would be otherwise very difficult.
There are, however, several interesting questions still to be addressed. In particular, for such systems, it is known that the dilatation operator at one loop can be related to an integrable Hamiltonian which possesses range two interaction. The range of interaction of these Hamiltonians increases with the number of loops and the process of constructing such long-range deformations perturbatively is well understood. How to obtain the Lax operator and the R-matrix, (both objects of fundamental importance in integrability) that generate such Hamiltonians was, however, still unknown.
In this talk, after an introduction about integrability in the context of N=4 SYM I will explain how to construct these operators and why they are useful, and mention some possible applications of our method in different problems.
Based on arXiv: 2206.08390, in collaboration with M. de Leeuw.