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

该合作奖资助纽约城市大学城市学院的V.P. Nair教授和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，与宇宙有关的广义相对论和与物质微观结构有关的量子理论取得了里程碑式的成就。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。黑洞内部和夸克结合形成原子核是两个人们知之甚少的例子。这个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者提供理想的培训。通过在城市学院和雷曼学院之间开展一个联合项目，我们达到了一个临界质量，可以吸引大量的学生，尤其是来自少数民族和代表性不足的群体的学生，这些学生在两所学院的学生群体中都占很大一部分。从技术上讲，这个项目进一步研究了一种新的流体动力学公式，侧重于对称结构。它详细阐述了先前发起的研究2+1维规范理论的技术及其在四维现实情况下的推广。由Kabat教授、Nair教授和其他人开发的新的计算技术将用于探索自旋和新的边界条件对卡西米尔力的影响。将使用最近开发的技术探索“模糊”（非交换）空间的场论的各个方面，最终目标是在大n（连续体）极限中捕获非摄动效应的有效作用。最后，AdS/CFT对应将被用作量子引力的精确公式，以研究局部体物理如何从CFT中产生。Kabat及其合作者先前的工作依赖于1/N摄动理论来表示CFT中的局部大块可观测值，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，并研究黑洞在有限N处的体局部性失效和宇宙学。

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.