Symmetries in string theory and quantum gravity

弦理论和量子引力中的对称性

• 批准号: SAPIN-2017-00025
• 负责人: Harrison, Sarah
• 金额: $ 0.28万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Subatomic Physics Envelope - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=762484
• 关键词: Symmetries; string; theory; quantum; gravity

Symmetries are a powerful tool which helps us organize our understanding of the most basic physical systems. I propose to use fascinating new mathematical insights to investigate fundamental aspects of string theory and quantum gravity. These insights relate large, discrete symmetry groups to basic structures underlying string theory, algebra, geometry, and number theory . The kinds of symmetries I propose to focus on underlie a fascinating and mysterious relation between modular objects and finite groups known as “moonshine.” The first example of this relation, uncovered in the 1980s and dubbed monstrous moonshine, denotes a connection between certain modular forms in number theory and the representation theory of the monster group, the largest of the sporadic finite simple groups. Many aspects of this relationship are elucidated by the existence of a "monster module," which is intimately connected to string theory and 2d conformal field theory. Yet many mysteries remain.A recent and as of yet unexplained discovery suggests that moonshine may have a fundamental relation to aspects of string theory and quantum gravity--from holography to black holes. In 2010, three physicists observed that dimensions of representations of M24, one of the sporadic finite simple groups, appear as coefficients of a mock modular form counting BPS states in the elliptic genus of string theory on K3 surfaces. K3 surfaces, long important objects in algebraic geometry, also underlie many important constructions in string theory, from supersymmetric string vacua to examples of holography, to microscopic descriptions of extremal black holes.I propose to investigate what these deep mathematical connections can teach us about three aspects of string theory and quantum gravity: string vacua, holographic theories in three dimensions, and supersymmetric black holes. Firstly, I propose to ask whether there is a new way to formulate string vacua based on symmetries or underlying mathematical and geometric structure, shedding light on fundamental aspects of string theory and the physical origin of many fascinating results in mathematics.Secondly, I propose to investigate recently uncovered connections between moonshine modules and holographic theories of gravity in three dimensions. In particular, I propose to investigate the physical interpretation of the underlying group- and number-theoretic structures, and understand to what extent these structures can lead to a general description of families holographic theories of gravity in three dimensions, elucidating universal aspects of quantum gravity and black hole physics. Finally, I propose to study relationships between mock modular forms, geometry, and moonshine modules which arise in the context of string-theoretic constructions of extremal black holes. This can lead to new ways of thinking about quantum black holes and their microstates.

对称性是一个强大的工具，可以帮助我们组织对最基本的物理系统的理解，我建议使用令人着迷的新数学见解来研究弦理论和量子引力的基本方面，这些见解将大型离散对称群与弦的基本结构联系起来。理论、代数、几何和数论。我建议重点研究模块化对象和有限群之间一种令人着迷且神秘的关系，这种关系被称为“moonshine”，这是在 20 世纪 80 年代发现的。被称为“怪物月光”，表示数论中某些模形式与怪物群表示论之间的联系，怪物群是最大的零星有限单群，这种关系的许多方面都是通过“怪物模”的存在来阐明的。与弦理论和二维共形场论密切相关，但仍然存在许多谜团。最近的一项尚未解释的发现表明，月光可能与弦理论和量子引力的各个方面有根本的关系。 2010 年，三位物理学家观察到，零星有限单群之一 M24 的表示维数出现在 K3 表面上的弦理论椭圆属中计算 BPS 态的模拟模形式的系数。 ，代数几何中长期重要的对象，也是弦理论中许多重要结构的基础，从超对称弦真空到全息术的例子，再到微观描述我建议研究这些深刻的数学联系可以告诉我们弦理论和量子引力的三个方面：弦真空、三维全息理论和超对称黑洞。基于对称性或基础数学和几何结构来制定弦真空的新方法，揭示了弦理论的基本方面以及数学中许多令人着迷的结果的物理起源。其次，我建议研究最近发现的 Moonshine 模块和特别是，我建议研究潜在的群论和数论结构的物理解释，并了解这些结构在多大程度上可以导致对三个维度的引力全息理论的一般描述。最后，我建议研究在极值黑洞的弦理论结构中出现的模拟模形式、几何和月光模之间的关系，这可能会产生新的结果。的方式思考量子黑洞及其微观状态。