Baxter Q-operators and supersymmetric gauge theories

这个科学项目涉及量子可积模型及其与规范理论的关系的研究。它的动机是不断增长的必要性，彻底和深入了解N=4的超级杨-米尔斯理论和N=6的超级陈-西蒙斯理论背后的可积结构，这可能最终允许这些超对称规范理论的非微扰制定。该建议包含两个相互关联但可以并行研究的主要研究主题。第一个主题的目标是通过结合非紧自旋链的Q算子构造和规范理论的著名量子谱曲线，使Q算子方法适用于N=4的超杨-米尔斯理论。第二个主题的目标是发展正交辛李超代数的自旋链的Q-算子构造，其结果可以从相应的N=2 π规范理论的Seiberg-Witten曲线中提取。特别地，这样的Q-算子出现在N=6的超陈-西蒙斯理论中。我们希望这个项目将揭示N=4的超级杨-米尔斯理论在有限耦合下的可积模型，同时也为将Q算子技术应用于N=6的超级陈-西蒙斯理论打开了大门。除此之外，我们的研究将使我们更接近于一般李代数自旋链的Q-算子构造的普遍公式。

This scientific project concerns the study of quantum integrable models and their relations to gauge theories. It is motivated by the growing necessity for a thorough and deep understanding of the integrable structures behind N=4 super Yang-Mills theory and N=6 super Chern-Simons theory which may ultimately allow for a non-perturbative formulation of these supersymmetric gauge theories. The proposal contains two major research themes which are interrelated but can be investigated in parallel. The goal of the first theme is to make Q-operator methods available for N=4 super Yang-Mills theory by combining the known Q-operator construction for non-compact spin chains and the celebrated Quantum Spectral Curve of the gauge theory. The goal of the second theme is to develop the Q-operator construction of spin chains for orthosymplectic Lie superalgebras using results which can be extracted from the Seiberg-Witten curve of the corresponding N=2 quiver gauge theories. In particular, such Q-operators appear in N=6 super Chern-Simons theory. We hope that this project will reveal the underlying integrable model of N=4 super Yang-Mills theory at finite coupling but also open the door to apply Q-operator techniques to N=6 super Chern-Simons theory. Apart from that, our studies shall bring us closer to a universal formulation of the Q-operator construction of spin chains for general Lie algebras.