Elliptic Stable Envelopes and R-matrices for Superspin Chains from 3d N=2 Gauge Theories (23rit110)


Nafiz Ishtiaque (IHES)

Seyed Faoogh Moosavian (McGill University)

Yehao Zhou (University of Tokyo)


The Banff International Research Station will host the "Elliptic Stable Envelopes and R-matrices for Superspin Chains from 3d N=2 Gauge Theories" workshop in Banff from July 9 to July 23, 2023.

Integrable spin chains are quantum mechanical models based on lattices that can be solved exactly. They play a crucial role in our understanding of how to model physical systems, such as magnets and other solid-state materials, using quantum mechanics. The Bethe/Gauge correspondence is a remarkable duality between such integrable spin chains and much more complicated quantum field theories (QFTs). This correspondence highlights that many QFTs with supersymmetry can be modeled by integrable spin chains at low energy. This provides valuable insight into the dynamics of QFTs.

The Bethe/Gauge correspondence has been studied extensively for many spin chains whose symmetry is given by classical bosonic Lie algebras. This has also inspired interesting new mathematics related to the representation theory of quantum groups. In our current project, we are trying to extend this correspondence for Lie superalgebras by computing certain observables in a 3d $\mathcal N = 2$ supersymmetric field theories inspired by a string theoretic explanation of the Bethe/Gauge correspondence.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).