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

“这个奖项是根据2009年美国复苏和再投资法案(公法111-5)资助的。”这项建议涉及理论物理学中一些相互关联的研究课题，并建立在私人投资机构早些时候开发的方法和结果的基础上。具体地说，将在哈密顿方法的基础上研究(2+1)维的杨-米尔斯理论的新方向。这将包括研究有限的温度效应。我们将研究将引力理解为非对易的Chern-Simons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。用于计算Casimir能量的广义多次反射展开式将被用来处理各种问题，例如介质边界和由于额外维度而对四维真空能量的修正的计算。将探索N=8爱因斯坦超引力的旋量弦描述，并进行更大幅度的旋量计算。通过非对易Wess-Zumino边界作用量，寻求高维费米子系统的最小玻色化，并解决与物理相关的模型。我们将研究环形量子霍尔系统的非对易Chern-Simons描述的物理态和性质。将发展广义非阿贝尔流体力学的相空间和算符方法，并可能应用于夸克-胶子等离子体等系统。我们将研究ADS/CFT对应中黑洞的性质，并详细指出半经典引力近似的缺陷。将建立暗能量和修正引力的模型，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重力精度测试的观测结果。该项目将研究早期宇宙模型中尺度因子振荡的弦动力学，并预测宇宙扰动的光谱。更广泛的影响如下：由于主题与弦理论、场论、凝聚态物理和数学物理有重叠的领域，该项目可以帮助在不同的子学科之间发展协同。该项目还具有培养、教学和培养人才的作用。这个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机会，让他们作为一个共享研究兴趣、资源、研讨会和博士后助理的小组发挥作用。这两所大学现在都处于招生增加的阶段，通过帮助培养一个积极的研究环境，该项目可以对吸引本科生进入物理专业产生积极影响。考虑到这两个校区学生群体的人口统计情况，少数族裔和代表性不足的群体尤其如此。

"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.