Separation of variables and correlation functions in high-rank integrable systems

Abstract

The spectral problem for N=4 Super Yang-Mills can be formulated as a set of quantisation conditions on a handful of functions called Q-functions. Recent analysis suggests that the Q-functions can be used as simple building blocks for 3-point correlation functions which closely resembles the situation in quantum integrable spin chains. In this talk I will describe the recently developed Functional Separation of Variables (FSoV) technique which is based on the famous Baxter TQ equation. This is a new tool for computing correlation functions in integrable models, and is applicable to both spin chains and 4D QFTs at finite coupling alike and naturally expresses observables as simple expressions in Q-functions. I will discuss new results obtained using this approach, in particular the computation of a complete family of correlation functions in high-rank non-compact SL(N) spin chains. Based on 2011.08229 and soon-to-appear work with N. Gromov and N. Primi.