Collaborative Research: Topics in Gauge Theory, Gravity and String Cosmology

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。该提案涉及理论物理学中许多相互关联的研究主题，并建立在PI早期开发的方法和结果的基础上。具体来说，杨米尔斯理论在（2+1）维的新方向将进行研究，建立在哈密顿方法。 这将包括研究有限温度效应。将研究把引力理解为非对易的陈-西蒙斯理论的大N极限的问题，并寻求对应于大N极限的黑洞的理论的解。计算卡西米尔能量的广义多重反射展开将用于解决各种问题，例如介电边界和由于额外维度对四维真空能量的修正计算。一个扭量弦描述N = 8爱因斯坦超引力将探讨和扭量计算更多的振幅将追求。通过非交换Wess-Zumino作用与边界的高维费米子系统的最小玻色化将被寻求，物理相关的模型将被处理。 我们将研究环形量子霍尔系统的非对易陈-西蒙斯描述的物理状态和性质。 一个相空间和运营商的方法来推广非阿贝尔流体力学将开发，与可能的应用系统，如夸克胶子等离子体。我们将研究黑洞在AdS/CFT对应中的性质，并详细讨论半经典引力近似的失效。将开发暗能量和修正引力模型，其中四维洛伦兹不变性仅在低能量下有效，并将分析它们对暗能量和引力精确测试的观测结果。 研究早期宇宙模型的弦动力学，其中尺度因子振荡，并预测宇宙学扰动的频谱。更广泛的影响如下：由于该主题与弦理论、场论、凝聚态物理学和数学物理学有重叠的领域，该项目可以帮助在不同的分支学科之间发展协同作用。该项目还具有培训、教学和培养人才的作用。 这个项目是在城市学院和雷曼学院之间建立合作的重要，创造了两个学院的高能理论家作为一个小组共享研究兴趣，资源，研讨会和博士后同事的机会。这两所学院目前都处于增加学生入学人数的阶段，通过帮助营造活跃的研究环境，该项目可以对吸引本科生进入物理学领域产生积极影响。考虑到两个校区学生的人口统计数据，对于少数民族和代表性不足的群体来说尤其如此。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). This proposal involves a number of interrelated topics of study in theoretical physics and builds on methods and results developed earlier by the PIs. Specifically, new directions for Yang-Mills theories in (2+1) dimensions will be studied, building on the Hamiltonian approach. This will include studying finite temperature effects. The problem of understanding gravity as a large-N limit of a non-commutiative Chern-Simons theory will be studied and solutions of the theory corresponding to a black hole in the limit of large N will be sought. A generalized multiple reflection expansion for calculating the Casimir energy will be used to address various problems, such as dielectric boundaries and the calculation of corrections to four-dimensional vacuum energy due to extra dimensions. A twistor string description of N = 8 Einstein supergravity will be explored and twistor calculations of more amplitudes will be pursued. The minimal bosonization of a higher-dimensional fermion system via non-commutative Wess-Zumino action with boundaries will be sought, and physically relevant models will be tackled. The physical states and properties of the non-commutative Chern-Simons description of the toroidal quantum Hall system will be investigated. A phase space and operator approach to generalized non-abelian fluid mechanics will be developed, with possible applications to systems such as the quark-gluon plasma. Properties of black holes in the AdS/CFT correspondence will be investigated and the failure of the semi-classical gravity approximation will be worked out in detail. Models for dark energy and modified gravity in which four-dimensional Lorentz invariance is only valid at low energies will be developed and their observational consequences for dark energy and precision tests of gravity will be analyzed. String dynamics of models of the early universe in which the scale factors oscillate will be investigated, and predictions for the spectrum of cosmological perturbations will be worked out.The broader implications are as follows: since the subject matter has areas of overlap with string theory, field theory, condensed matter physics and mathematical physics, the project can help develop synergy within different sub-disciplines. The project also has a role in training, teaching and fostering talent. This project is important in establishing collaboration between City College and Lehman College, creating the opportunity for the high energy theorists of two colleges to function as a group sharing research interests, resources, seminars, and postdoctoral associates. Both colleges are now in a phase of increasing student enrollment, and by helping to foster an active research environment this project can have a positive impact on attracting undergraduate students into physics. Given the demographics of the student body at the two campuses, this will be particularly true for minority and under-represented groups.