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

合作研究：规范论、引力和弦宇宙学主题

• 批准号: 0855515
• 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: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-01 至 2012-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0855515&HistoricalAwards=false
• 关键词: Collaborative; Research; Topics; Gauge; Theory

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.

该奖项根据 2009 年《美国复苏和再投资法案》（公法 111-5）提供资金。该提案涉及理论物理领域的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，将在哈密顿方法的基础上研究 (2+1) 维度的杨-米尔斯理论的新方向。 这将包括研究有限温度效应。将研究将引力理解为非交换陈-西蒙斯理论的大N极限的问题，并寻求与大N极限中的黑洞相对应的理论的解决方案。用于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，例如电介质边界以及由于额外维度而对四维真空能量进行校正的计算。将探索 N = 8 爱因斯坦超引力的扭量弦描述，并将追求更多振幅的扭量计算。将寻求通过具有边界的非交换 Wess-Zumino 作用实现高维费米子系统的最小玻色化，并解决物理相关模型。 将研究环形量子霍尔系统的非交换陈-西蒙斯描述的物理状态和性质。 将开发广义非阿贝尔流体力学的相空间和算子方法，并可能应用于夸克-胶子等离子体等系统。将研究 AdS/CFT 对应关系中黑洞的性质，并详细解决半经典重力近似的失败问题。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密测试的观测结果。 将研究尺度因子振荡的早期宇宙模型的弦动力学，并对宇宙扰动谱进行预测。更广泛的含义如下：由于该主题与弦理论有重叠的领域，场论、凝聚态物理和数学物理，该项目可以帮助发展不同子学科之间的协同作用。该项目还具有培训、教学和培养人才的作用。 该项目对于建立城市学院和雷曼学院之间的合作非常重要，为两所学院的高能量理论家创造了作为一个团队共享研究兴趣、资源、研讨会和博士后的机会。两所学院目前都处于增加学生入学率的阶段，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群体的人口统计数据，对于少数族裔和代表性不足的群体来说尤其如此。