Infinite-Dimensional Spin Chains from Gauge Theory

Explore the fascinating world of infinite-dimensional spin chains and their connections to gauge theory in this comprehensive M-Seminar lecture by Nikita Nekrasov from the Simons Center. Delve into the history and significance of spin chains in quantum mechanics, starting with the Bethe ansatz for the Heisenberg spin chain Hamiltonian. Discover how this foundational concept has inspired physicists and mathematicians for nearly a century, leading to groundbreaking developments such as quantum groups. Examine several infinite-dimensional generalizations of spin chains and their crucial role in understanding strong interactions of elementary particles, including L.Lipatov's reggeized gluons, planar N=4 super-Yang-Mills anomalous dimensions, and surface defects in N=2 super-QCD. Gain insights into the mathematical aspects of these concepts, exploring the generating function of equivariant DT-type invariants defined via the moduli spaces of parabolic sheaves on complex surfaces. Uncover the surprising appearances of Hecke operators from geometric and analytic Langlands programs, and learn how gauge theory allows for their generalization beyond the critical level. Based on recent collaborative work with Saebyeok Jeong, Norton Lee, and ongoing research with Andrey Grekov, this 1-hour 29-minute lecture offers a deep dive into the cutting-edge intersection of quantum mechanics, gauge theory, and mathematics.