Collaborative Research: Investigations on Fluids, Gauge Fields, Matrix Models and Gravity

合作研究：流体、规范场、矩阵模型和重力的研究

• 批准号: 1519449
• 负责人: V Nair
• 金额: $ 48万
• 依托单位: CUNY City College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-15 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1519449&HistoricalAwards=false
• 关键词: Collaborative; Research; Investigations; Fluids; Gauge

This Collaborative award funds the research activities of Professors V.P. Nair and A.P. Polychronakos at the City College of the City University of New York, and Professor Daniel Kabat at Lehman College of the City University of New York.Physics made tremendous strides during the 20th century, with the landmark achievements of general relativity, relevant to the universe at large, and quantum theory, relevant to the microscopic structure of matter. Further progress calls for studying situations in which our understanding of these theories is incomplete. The interior of a black hole and the binding of quarks to form atomic nuclei are two examples of poorly understood situations. This research program brings powerful mathematical tools to bear on these and related problems. As a result, research in this area advances the national interest by promoting the progress of science in one of its most fundamental directions: the discovery and understanding of new physical laws. Moreover, this research will involve graduate and undergraduate students, providing ideal training for the next generation of scientists and science educators. By running a joint program between City College and Lehman College we achieve a critical mass and can draw on a large pool of students, especially from minority and under-represented groups which are a large part of the student body at both colleges.More technically, this project furthers an investigation into a new formulation of fluid dynamics focusing on symmetry structures. It elaborates on previously initiated techniques to study gauge theories in 2+1 dimensions and their extension to the realistic case of four dimensions. New calculational techniques, developed by Professors Kabat, Nair and others, will be used to explore the effects of spin and novel boundary conditions on the Casimir force. Various aspects of field theory on "fuzzy" (noncommutative) spaces will be explored using recently developed techniques, the eventual goal being an effective action which captures nonperturbative effects in the large-N (continuum) limit. Finally the AdS/CFT (Anti-de Sitter Space/Conformal Field Theory) correspondence will be used as a precise formulation of quantum gravity to investigate how local bulk physics emerges from the CFT. Previous work by Kabat and collaborators, relying on 1/N perturbation theory to represent local bulk observables in the CFT, will be extended to higher orders in 1/N and used to constrain CFT four-point functions. The entanglement structure of the CFT will be used to study the black hole interior, and the failure of bulk locality at finite N for black holes and cosmology will be investigated.

该合作奖资助纽约城市大学城市学院的V.P.Nair和A.P.Polychronakos教授以及纽约城市大学雷曼学院的Daniel Kabat教授的研究活动。物理学在20世纪取得了巨大的进步，取得了与整个宇宙相关的广义相对论和与物质微观结构相关的量子理论的里程碑式的成就。进一步的进展需要研究我们对这些理论的理解不完整的情况。黑洞的内部和夸克的结合形成原子核是两个鲜为人知的情况。这项研究计划带来了强大的数学工具来处理这些问题和相关问题。因此，这一领域的研究通过促进科学最基本的方向之一--发现和理解新的物理定律--来促进国家利益。此外，这项研究将涉及研究生和本科生，为下一代科学家和科学教育工作者提供理想的培训。通过城市学院和雷曼学院之间的联合项目，我们达到了一个临界的质量，并可以吸引大量的学生，特别是来自少数群体和代表不足的群体的学生，这些群体是两所大学学生群体的一大部分。更严格地说，这个项目进一步调查了专注于对称结构的流体动力学的新公式。它详细阐述了以前开创的研究2+1维规范理论的技术，以及它们对四维现实情况的扩展。由Kabat教授、Nair教授和其他人开发的新计算技术将用于探索自旋和新的边界条件对Casimir力的影响。我们将使用最新发展的技术探索“模糊”(非交换)空间上场论的各个方面，最终目标是在大N(连续统)极限中捕捉非微扰效应的有效行动。最后，ADS/CFT(反德西特空间/共形场理论)对应将被用作量子引力的精确公式，以研究局域体物理是如何从CFT中出现的。Kabat和他的合作者以前的工作依赖于1/N微扰理论来表示CFT中的局部整体可观测量，将其扩展到1/N的高阶，并用于约束CFT的四点函数。CFT的纠缠结构将被用来研究黑洞内部，并将研究黑洞和宇宙学在有限N处的体局域性失效。