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: 1519705
• 负责人: Daniel Kabat
• 金额: $ 13.5万
• 依托单位: Research Foundation Of The City University Of New York (Lehman)
• 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 2018-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1519705&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 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.

该合作奖项资助副教授的研究活动。纽约城市大学城市学院的 Nair 和 A.P. Polychronakos 以及纽约城市大学雷曼学院的 Daniel Kabat 教授。物理学在 20 世纪取得了巨大进步，广义相对论取得了里程碑式的成就，与整个宇宙以及与物质微观结构相关的量子理论。进一步的进步需要研究我们对这些理论的理解不完整的情况。黑洞的内部和夸克结合形成原子核是我们知之甚少的情况的两个例子。该研究项目带来了强大的数学工具来解决这些及相关问题。 因此，这一领域的研究通过促进科学在其最基本方向之一的进步来促进国家利益：发现和理解新的物理定律。 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，我们达到了临界质量，并且可以吸引大量学生，特别是来自少数族裔和代表性不足群体的学生，这些群体在两所学院的学生群体中占很大一部分。该项目进一步研究了以对称结构为重点的流体动力学新公式。它详细阐述了先前提出的研究 2+1 维度规范理论的技术及其扩展到四个维度的实际情况。卡巴特教授、奈尔教授等人开发的新计算技术将用于探索自旋和新边界条件对卡西米尔力的影响。将使用最近开发的技术来探索“模糊”（非交换）空间场论的各个方面，最终目标是捕获大 N（连续体）极限中的非微扰效应的有效作用。 最后，AdS/CFT 对应关系将用作量子引力的精确公式，以研究局域体物理如何从 CFT 中产生。 Kabat 及其合作者之前的工作，依靠 1/N 微扰理论来表示 CFT 中的局部批量可观测量，将扩展到 1/N 的更高阶，并用于约束 CFT 四点函数。 CFT的纠缠结构将用于研究黑洞内部，并研究黑洞和宇宙学在有限N处的体局域性失效。