Nikita Nekrasov (Simons Center); April 4, 2024
Spin chains are quantum mechanical models of interacting degrees of freedom, such as (anti)ferromagnetic atoms. The celebrated Bethe ansatz for the eigenstates of the Heisenberg spin chain Hamiltonian has been a source of inspiration for physicists and mathematicians for almost a century now, leading to the invention of quantum groups, among other achievements. In my talk I will describe several infinite-dimensional generalizations of spin chains, which are believed to play an important role in the studies of strong interactions of elementary particles: L.Lipatov's reggeized gluons, planar N=4 super-Yang-Mills anomalous dimensions and, closer to the seminar's theme: surface defects in N=2 super-QCD. Mathematically, the latter is the generating function of equivariant DT-type invariants defined via the moduli spaces of parabolic sheaves on complex surfaces. Surprisingly, the Hecke operators of geometric and analytic Langlands programs make appearances, and gauge theory allows them to generalize outside the critical level. Based on the recent work with Saebyeok Jeong, Norton Lee, and on the recent work and work in progress with Andrey Grekov.