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Baxter Q-operators and supersymmetric gauge theories

Baxter Q 算子和超对称规范理论

基本信息

批准号：
416527151
负责人：
Dr. Rouven Frassek
金额：
--
依托单位：
Laboratoire de Physique Théorique
依托单位国家：
德国
项目类别：
Research Fellowships
财政年份：
2019
资助国家：
德国
起止时间：
2018-12-31 至 2020-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/416527151?language=en
关键词：
Baxter operators supersymmetric gauge theories

项目摘要

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.

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。它的动机是对N=4超级Yang-Mills理论和N=6超级chen - simons理论背后的可积结构的透彻和深刻理解的日益增长的必要性，这可能最终允许这些超对称规范理论的非摄动表述。该提案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已知的非紧自旋链的q算子构造和规范理论中著名的量子谱曲线，使q算子方法可用于N=4超级Yang-Mills理论。第二个主题的目标是利用相应的N=2颤振规范理论的Seiberg-Witten曲线的结果，发展正辛李超代数自旋链的q算子构造。特别地，这样的q算子出现在N=6超级chen - simons理论中。我们希望该项目将揭示N=4超级Yang-Mills理论在有限耦合下的潜在可积模型，并为将q算子技术应用于N=6超级chen - simons理论打开大门。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算子构造的通用公式。