Strings, Branes and the Search for Unification

弦、膜和对统一的追求

• 批准号: 0906222
• 负责人: Melanie Becker
• 金额: $ 105万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0906222&HistoricalAwards=false
• 关键词: Strings; Branes; Search; Unification

The three researchers on this proposal propose a program investigating fundamental aspects of string theory and M-theory and their implications for particle phenomenology and cosmology. One aspect of this project deals with the construction and implications for phenomenology of flux backgrounds for heterotic strings, which they denote by torsional heterotic geometries. The heterotic string is a natural setting to construct models of particle phenomenology. However, the role played by background H-flux has not been unraveled yet, even though it may profoundly influence the 4d low-energy effective action. In this project the PIs employ a strategy to obtain the first large class of torsional heterotic geometries by explicitly constructing their metric. The number of torsional heterotic geometries turns out to be of the same order of magnitude as the number of type II flux backgrounds. The explicit examples display an N=2,1,0, supersymmetry in 4d. Flux changes the 4d phenomenology and the PIs are investigating the implications of this new strategy. They propose strategies to obtain chiral matter and novel ways to break the E8 gauge symmetry to the standard model gauge group. These backgrounds stand a much better chance of admitting tractable world-sheet descriptions compared to the type II counterparts. The precise implications of torsional geometries for algebraic geometry such as the calculation of the exact moduli space of torsional geometries, the resolution of singularities, the construction of vector bundles and ultimately three-generation models with stabilized moduli is proposed. Evidence of string theory from cosmology will be explored in terms of a brane inflation model. String theory models make predictions for gravitational radiation and lead to strong non-Gaussianities in the cosmic microwave background. Several aspects of the duality between M-theory compactifications to 4d space-time and its boundary conformal field theories (CFT) will also be explored. The research also includes a systematic construction and possible string/M-theory embedding of new supergravities in diverse dimensions, exploration of infinite dimensional symmetries, and their implications for integrability in string theory in nontrivial backgrounds. Finally, the important question of the uniqueness of string theory as a candidate for a quantum theory of gravity will be addressed in the context of 3d quantum gravity and its dual CFT. The broader impacts of the project are related to the importance of testing string theory as theory that can describe experiments. The PIs are looking for ways to understand the experimental tests for Cosmology and particle physics. In the LHC era and with new satellites becoming available, it is vital to work out the connections between physics at the Planck scale and TeV scale physics, while advancing our knowledge in string cosmology. The final goal of this project is to unravel the imprints of high-energy physics onto our 4d world. At the same time the program is expected to have a profound impact on different areas of mathematics. Two of the PIs have just written an important book on string theory and M theory with John Schwartz, one of the founders of superstring theory. All three PIs are involved in disseminating information about string theory by giving talks at workshops and conferences as well as organizing workshops. They are also involved in collaborations with mathematicians to understand the topology and geometry of string theory.

这项提议的三位研究人员提出了一个项目，研究弦理论和M理论的基本方面，以及它们对粒子现象学和宇宙学的影响。这个项目的一个方面是关于杂化弦的磁通背景的构造和现象学的含义，它们由扭转杂化几何来表示。杂化弦是构建粒子现象学模型的自然环境。然而，背景氢通量所起的作用尚未被揭示，尽管它可能深刻地影响4d低能有效作用。在这个项目中，PI采用了一种策略，通过显式构造它们的度量来获得第一大类扭转杂化几何。扭转杂化几何构型的数量与第二类磁通背景的数量具有相同的数量级。显式例子表明N=2，1，0在4d内具有超对称性。通量改变了4D现象学，PI正在研究这一新策略的含义。他们提出了获得手性物质的策略和打破E8规范对称性到标准模型规范群的新方法。与第二类背景相比，这些背景有更好的机会接受容易理解的世界页描述。提出了扭转几何对代数几何的精确含义，如扭转几何的精确模空间的计算、奇点的分解、矢丛的构造以及最终具有稳定模的三代模型。来自宇宙学的弦理论的证据将以膜膨胀模型的形式进行探索。弦理论模型预测了引力辐射，并在宇宙微波背景中导致了强烈的非高斯性。还将探讨M理论压缩到4D时空与其边界共形场理论(CFT)之间的对偶性的几个方面。这项研究还包括不同维度上新超引力的系统构建和可能的弦/M理论嵌入，无限维对称性的探索，以及它们对弦理论在非平凡背景下的可积性的影响。最后，弦理论作为量子引力理论候选者的唯一性这一重要问题将在三维量子引力及其对偶CFT的背景下得到解决。该项目的更广泛影响与测试弦理论作为描述实验的理论的重要性有关。PI们正在寻找理解宇宙学和粒子物理学实验测试的方法。在大型强子对撞机时代，随着新卫星的出现，弄清普朗克尺度的物理和TeV尺度的物理之间的联系，同时推进我们在弦宇宙学方面的知识是至关重要的。这个项目的最终目标是揭开高能物理在我们的4d世界上的印记。与此同时，该项目预计将对数学的不同领域产生深远影响。其中两位PI刚刚与超弦理论的创始人之一约翰·施瓦茨共同撰写了一本关于弦理论和M理论的重要著作。所有三个私人助理都通过在研讨会和会议上发表演讲以及组织研讨会来传播弦理论的信息。他们还参与了与数学家的合作，以了解弦理论的拓扑和几何。