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Yangian Symmetry in Quantum Gauge Field Theory

量子规范场论中的杨对称性

基本信息

批准号：
324161040
负责人：
Professor Dr. Jan Plefka
金额：
--
依托单位：
Arbeitsgruppe Quantenfeld- und Stringtheorie
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2016
资助国家：
德国
起止时间：
2015-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/324161040?language=en
关键词：
Yangian Symmetry Quantum Gauge Field

项目摘要

Our understanding of nature at its deepest level is governed by symmetries. This proposal aims at studying hidden symmetries in quantum field theory going beyond the established space-time symmetries of the Poincare group and its supersymmetric or conformal extensions. Our approach is divided into three research strands. They are grounded on our discovery of an infinite dimensional symmetry for the S-matrix of maximally supersymmetric gauge theory in four dimensions, known as the Yangian. In the first strand we will investigate the implication of the hidden symmetry for smooth Wilson loop observables, providing novel tools for exact, non-perturbative results. In the second strand we will study the Yangian symmetry as a classical symmetry of the action rather than as a dynamical symmetry of quantum observables. This aims at a classification of Yangian symmetric quantum field theories in four dimensions and is expected to constrain the quantum effective action. Finally, we shall analyze Yangian symmetry in 4D quantum field theory from the viewpoint of a generalized Haag-Lopuszanski-Sohnius theorem upon allowing for a non-trivial co-product. The ultimate goal of these research strands is to innovate the standard perturbative approach in quantum field theory by expanding in perturbations about an integrable model, such as N=4 gauge theory.

我们对自然最深层次的理解是由对称性所支配的。这个建议的目的是研究量子场论中隐藏的对称性，超越庞加莱群及其超对称或共形扩展的时空对称性。我们的方法分为三个研究环节。它们的基础是我们发现了四维最大超对称规范理论的S-矩阵的无穷维对称性，称为杨阶。在第一链中，我们将调查光滑威尔逊回路可观测量的隐藏对称性的含义，提供精确的，非微扰的结果的新工具。在第二条链中，我们将研究作为经典对称性的作用量，而不是作为量子观测的动力学对称性的杨氏对称性。这旨在对四维中的扬格对称量子场论进行分类，并有望约束量子有效作用量。最后，我们将从广义Haag-Lopuszanski-Sohnius定理的观点分析4D量子场论中的Yangian对称性，该定理允许非平凡的余积。这些研究链的最终目标是通过扩展可积模型（如N=4规范理论）的微扰来创新量子场论中的标准微扰方法。