Strings, Branes and the Search for Unification

这三位研究人员提出了一个研究弦理论和M理论的基本方面及其对粒子现象学和宇宙学的影响的计划。这个项目的一个方面涉及的建设和影响的现象学的磁通背景的杂化弦，他们表示扭转杂化几何。杂化弦是构建粒子唯象模型的自然背景。然而，背景氢通量所起的作用还没有解开，即使它可能会深刻影响4d低能有效作用。在这个项目中，PI采用的策略，以获得第一大类的扭转杂化几何明确构建其度量。扭转杂种优势几何形状的数量原来是相同的数量级的II型通量背景的数量。明确的例子显示了一个N= 2，1，0，超对称在4d。Flux改变了4d现象学，PI正在研究这种新策略的含义。他们提出了获得手征物质的策略和打破标准模型规范群E8规范对称性的新方法。与第二类对应物相比，这些背景更有可能接受易处理的世界表描述。扭转几何的代数几何的精确含义，如扭转几何的精确模空间的计算，奇异性的解决方案，向量丛的建设，并最终与稳定的模的三代模型提出。弦理论从宇宙学的证据将探讨在膜膨胀模型。 弦理论模型预测了引力辐射，并导致宇宙微波背景中的强非高斯性。 M-理论紧化到4D时空和它的边界共形场论（CFT）之间的对偶性的几个方面也将被探讨。该研究还包括一个系统的建设和可能的弦/M理论嵌入新的超引力在不同的维度，探索无限维对称性，以及它们的影响，在非平凡的背景弦理论的可积性。最后，弦理论作为引力量子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可以描述实验的理论的重要性有关。PI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，在普朗克尺度和TeV尺度物理学之间建立联系至关重要，同时推进我们在弦宇宙学方面的知识。这个项目的最终目标是解开高能物理在我们4d世界上的印记。同时，该计划预计将对数学的不同领域产生深远的影响。其中两个PI刚刚和超弦理论的创始人之一约翰·施瓦茨一起写了一本关于弦理论和M理论的重要著作。所有三个PI都参与传播有关弦理论的信息，在研讨会和会议上发表演讲，以及组织研讨会。 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。

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.