Niclai maps in super gauge theory and gravity

超规范理论和引力中的尼克莱图

• 批准号: 522280455
• 负责人: Professor Dr. Olaf Lechtenfeld
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/522280455?language=en
• 关键词: Niclai; maps; super; gauge; theory

In 1980 Hermann Nicolai discovered that globally supersymmetric theories can be characterized without fermionic degrees of freedom: The nonlocal purely bosonic theory obtained after integrating out all fermions (and potential ghosts) at any coupling g admits a nonlinear field transformation to the free theory (at g=0), the so-called Nicolai map. Alternatively, this map can be defined by equating the interacting correlation function of any field functional with the free correlation function of the inversely transformed field functional. In the early 1980s a perturbative construction scheme for the Nicolai map was developed in one, two and four spacetime dimensions, for Wess-Zumino models as well as for super Yang-Mills theory, by exponentiating a "coupling-flow operator" which induces an infinitesimal shift in the coupling. It led to an alternative formulation of supersymmetric perturbation theory, complementary to the standard super-space or component approach. The subject was all but forgotten until 2020, when Hermann Nicolai and collaborators revisited the map for super Yang-Mills theory, now also in higher dimensions, found that it exists only in the critical dimensions three, four, six and ten, and pushed its perturbative construction to (currently) fourth order. Since then, there has been a flurry of new results: a universal formula for the map, its non-uniqueness and ambiguities, criteria for its linearity, its gauge dependence, the large-order perturbation behavior and non-perturbative existence. In addition, we have seen applications to N=4 super Yang-Mills correlators, matrix models and the maximal supermembrane. These findings open a new perspective for a deeper structural analysis of the Nicolai map on one side and for practical applications to correlation functions in supersymmetry, supergauge theory and perhaps supergravity. This project has four parts. First, we plan to expand the Nicolai-map treatment of supersymmetric scalar theories. Specific topics here are the renormalization of the map, an extension to sigma models, the investigation of supersymmetry breaking, and nonrelativistic versions of the Nicolai map. The second part concerns super Yang-Mills theory. Here, we shall generalize the map to harmonic super-space, to supersymmetry-preserving gauge fixings, clarify the failure of linear maps in the light-cone gauge, and optimize the map for N=4 super Yang-Mills. Third, we will try to formulate a Nicolai map for supergravity, and fourth, we intend to revisit the super matrix model and the super-membrane, in order to overcome the technical obstacles with its quantum correlators via the Nicolai map in the small-tension limit. It is expected that successful completion of this project will establish the Nicolai map as a viable tool and a competitive calculational technique in supersymmetric quantum field theories and even offer a new way to quantize previously intractable cases like supergravity or the super-membrane.

1980年，Hermann Nicolai发现全局超对称理论可以在没有费米子自由度的情况下被表征：在任何耦合g下积分出所有费米子（和潜在幽灵）后得到的非局部纯玻色子理论承认了对自由理论（在g=0时）的非线性场变换，即所谓的Nicolai映射。或者，这个映射可以通过将任何场泛函的相互作用的相关函数等同于反变换的场泛函的自由相关函数来定义。在20世纪80年代早期，通过对“耦合-流动算子”进行幂运算，在耦合中引起无限小的位移，在一维、二维和四维时空中，为weiss - zumino模型以及超级Yang-Mills理论开发了Nicolai图的摄动构造方案。它导致了超对称微扰理论的另一种表述，补充了标准超空间或分量方法。直到2020年，这个主题几乎被遗忘了，当时赫尔曼·尼古拉和合作者重新审视了超级杨-米尔斯理论的地图，现在也是在更高的维度，发现它只存在于关键维度3、4、6和10，并将其微扰结构推到了（目前的）四阶。从那时起，出现了一系列新的结果：映射的通用公式，它的非唯一性和模糊性，它的线性准则，它的规范依赖性，大阶摄动行为和非摄动存在性。此外，我们还看到了N=4超级Yang-Mills相关器、矩阵模型和最大超膜的应用。这些发现为更深入地分析Nicolai地图的一侧结构，以及在超对称、超规范理论和超引力理论中相关函数的实际应用开辟了新的视角。这个项目有四个部分。首先，我们计划扩展超对称标量理论的nicolai映射处理。这里的具体主题是映射的重整化，sigma模型的扩展，超对称破缺的研究，以及尼古拉映射的非相对论版本。第二部分是超级杨-米尔斯理论。在这里，我们将映射推广到调和超空间，推广到保持超对称的规范固定，澄清光锥规范中线性映射的失效，并优化N=4个超级Yang-Mills的映射。第三，我们将尝试建立一个超重力的Nicolai图；第四，我们打算重新审视超矩阵模型和超膜，以克服其量子相关器在小张力极限下的Nicolai图的技术障碍。预计该项目的成功完成将使Nicolai图成为超对称量子场论中可行的工具和有竞争力的计算技术，甚至为超重力或超膜等以前难以解决的问题提供一种新的量化方法。