New Geometric Structures from String Theory

弦理论的新几何结构

• 批准号: EP/K034456/1
• 负责人: Christopher Hull
• 金额: $ 201.63万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2013
• 资助国家: 英国
• 起止时间: 2013 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FK034456%2F1
• 关键词: New; Geometric; Structures; String; Theory

Our proposed research is aimed towards discovering the mathematical structures underpinning the fundamental nature of matter, the origins of the universe and the quantum structure of spacetime each of which would be a revolution in science, with possible consequences as far-reaching as they were when matter was shown to be composed of atoms. Just as differential geometry was vital for Einstein's theory of gravity, the mathematics we are investigating could be an essential part of a revolution the formulation of string theory, with possible far-reaching consequences. Theoretical physics has long been central in motivating vital new directions in geometry. Recent research in string theory points to the existence of a rich class of remarkable new geometrical structures. The aim of the research is to develop the underlying unifying mathematics of these structures, laying the foundations for new areas of geometric study using tools and ideas from string theory and gauge theory. It is rare to find a new type of geometry that is both beautiful and tractable. Generalized geometry, introduced by Hitchin, is one such new example, and like others is strongly linked with ideas from physics. The overarching focus of our proposal will be the much larger set of ideas of which this is part, including extended geometries, doubled geometries, flux geometries, non-geometric spaces and holographic structures. We anticipate wide ranging applications across mathematical sciences from geometry and topology to algebra and number theory and mathematical physics.

我们提出的研究旨在发现支撑物质基本性质、宇宙起源和时空量子结构的数学结构，其中每一个都将是一场科学革命，其可能产生的影响与物质被证明是由原子组成时一样深远。正如微分几何对于爱因斯坦的引力理论至关重要一样，我们正在研究的数学也可能成为弦理论公式革命的重要组成部分，并可能产生深远的影响。长期以来，理论物理学一直是推动几何学重要新方向的核心。弦理论的最新研究指出存在一类丰富的、引人注目的新几何结构。该研究的目的是开发这些结构的基础统一数学，利用弦理论和规范理论的工具和思想为几何研究的新领域奠定基础。很难找到一种既美观又易于处理的新型几何形状。希钦提出的广义几何就是这样一个新例子，与其他例子一样，它与物理学思想密切相关。我们提案的首要重点将是更大的一组想法，这是其中的一部分，包括扩展几何、双重几何、通量几何、非几何空间和全息结构。我们预计在数学科学中会有广泛的应用，从几何和拓扑到代数和数论以及数学物理。

项目成果

The exceptional sigma model

• DOI: 10.1007/jhep04(2018)064
• 发表时间: 2018-02
• 期刊: Journal of High Energy Physics
• 影响因子: 5.4
• 作者: Alex S. Arvanitakis;Chris D. A. Blair

Spatially modulated and supersymmetric deformations of ABJM theory

• DOI: 10.1007/jhep04(2019)099
• 发表时间: 2018-12
• 期刊: Journal of High Energy Physics
• 影响因子: 5.4
• 作者: Igal Arav;J. Gauntlett;M. Roberts;C. Rosen

More large N limits of 3d gauge theories

3d 规范理论的更大 N 限制

• DOI: 10.1088/1751-8121/aa7e11
• 发表时间: 2017
• 期刊: Mathematical and Theoretical
• 作者: Anderson L

T-duality in (2, 1) superspace

(2, 1) 超空间中的 T 对偶性

• DOI: 10.1007/jhep06(2019)138
• 发表时间: 2019
• 期刊: Journal of High Energy Physics
• 影响因子: 5.4
• 作者: Abou-Zeid M

Quiver tails and N = 1 $$ \mathcal{N}=1 $$ SCFTs from M5-branes

来自 M5 膜的箭袋尾部和 N = 1 $$ mathcal{N}=1 $$ SCFT

• DOI: 10.1007/jhep03(2015)049
• 发表时间: 2015
• 期刊: Journal of High Energy Physics
• 影响因子: 5.4
• 作者: Agarwal P