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

该合作奖资助了纽约市立大学城市学院的V.P. Nair教授和A.P. Polychronakos教授以及纽约市立大学雷曼学院的Daniel Kabat教授的研究活动。物理学在20世纪取得了巨大的进步，广义相对论和量子理论取得了里程碑式的成就，与物质的微观结构有关。进一步的进展要求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两个我们知之甚少的例子。这项研究计划带来了强大的数学工具来承担这些和相关的问题。 因此，这一领域的研究通过促进科学在其最基本的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，我们达到了临界质量，可以吸引大量的学生，特别是来自少数民族和代表性不足的群体，他们是两所学院学生的很大一部分。更技术上，这个项目进一步研究了一种新的流体动力学公式，重点是对称结构。它详细阐述了以前发起的技术，研究规范理论在2 + 1维及其扩展到现实的情况下，四维。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边界条件对Casimir力的影响。场论的各个方面的“模糊”（非交换）空间将探讨使用最近开发的技术，最终目标是一个有效的行动，捕捉非微扰效应在大N（连续）的限制。 最后，AdS/CFT（Anti-de Sitter Space/Conformal Field Theory）对应将被用作量子引力的精确表述，以研究局域体物理如何从CFT中出现。 Kabat及其合作者先前的工作依赖于1/N微扰理论来表示CFT中的局部体观测量，将扩展到1/N的高阶，并用于约束CFT四点函数。 我们将利用CFT的纠缠结构研究黑洞内部，并研究黑洞和宇宙学在有限N处体定域性的失效。

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.