Conformal Field Theories in Holography and String Theory

全息术和弦理论中的共形场论

• 批准号: 2111748
• 负责人: Christoph Keller
• 金额: $ 22.5万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-09-01 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2111748&HistoricalAwards=false
• 关键词: Conformal; Field; Theories; Holography; String

There are four fundamental forces in the universe. The electromagnetic force and the two nuclear forces are described by Quantum Field Theory (QFT); the gravitational force is described by the theory of General Relativity (GR). String Theory aims to unify these four forces, while at the same time providing a quantum mechanical description of gravity. In this endeavor, quantum field theories that are scale invariant, so called conformal field theories (CFTs), are crucial: On the one hand they describe how strings move and interact; on the other hand, through the principle of holography, they can describe quantum gravity. The PI aims to deepen the understanding of string theory and QFTs by investigating such CFTs and their applications, with a focus on their mathematical structure and their connection to mathematics. The work aims to construct new examples of CFTs that can be used in string theory. In addition, this project will have a broader impact on education by offering suitable activities and research projects for undergraduate and graduate students, thereby introducing them to contemporary research. The PI will also work with the Center for Recruitment and Retention of Mathematics Teachers at the University of Arizona to develop modules that introduce high school students to quantitative thinking and mathematical reasoning in physics and other STEM disciplines.At a more technical level, the PI will develop 2D conformal perturbation theory with a focus on orbifold CFTs. He will use this to investigate the interplay between rational and irrational CFTs in moduli spaces of Calabi-Yau sigma models, and to investigate how the spectrum of holographic 2D CFTs such as symmetric orbifolds changes over their moduli space. He will also construct new holographic CFTs using permutation orbifolds and lattice orbifolds, which may lead to new examples of AdS/CFT dualities. He will particularly focus on CFTs with sparse light spectrum and extremal or near extremal CFTs. This research will rely on recent results from mathematics such as the theory of non-abelian orbifolds of vertex operator algebras.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

宇宙中有四个基本力量。电磁力和两个核力量通过量子场理论（QFT）描述；重力由一般相对论（GR）的理论描述。弦理论旨在统一这四个力，同时提供重力的量子机械描述。在这项工作中，量表不变的量子场理论（所谓的共形场理论（CFTS））至关重要：一方面，他们描述了字符串的移动和相互作用；另一方面，通过全息原则，它们可以描述量子重力。 PI的目的是通过研究此类CFT及其应用来加深对弦理论和QFT的理解，重点是它们的数学结构及其与数学的联系。该作品旨在构建可以在字符串理论中使用的CFT的新示例。此外，通过为本科生和研究生提供合适的活动和研究项目，该项目将对教育产生更大的影响，从而将其介绍给当代研究。 PI还将与亚利桑那大学的数学教师招聘和保留中心合作，以开发模块，这些模块会引入高中生在物理和其他STEM学科中的定量思维和数学推理。在更高的技术水平上，PI将开发出2D形式的触发理论，重点介绍ORBIFOLD CFTS。他将使用它来研究卡拉比Yau Sigma模型模量空间中合理和非理性CFT之间的相互作用，并研究全息2D CFT的频谱（例如对称轨道）在其模量空间上的变化。他还将使用置换的Orbifolds和Grattice Orbifolds构建新的全息CFT，这可能会导致ADS/CFT二元性的新示例。他将特别专注于稀疏光谱，极端或极端CFT的CFT。这项研究将依靠数学的最新结果，例如顶点操作员代数的非 - 亚伯利亚轨道理论。该奖项反映了NSF的法定任务，并被认为是通过基金会的智力优点和更广泛影响的审查标准通过评估来通过评估来支持的。

项目成果

Limits of Vertex Algebras and Large N Factorization

• DOI: 10.1007/s00220-023-04712-x
• 发表时间: 2023-04-11
• 期刊: COMMUNICATIONS IN MATHEMATICAL PHYSICS
• 影响因子: 2.4
• 作者: Gemunden，Thomas;Keller，Christoph A.
• 通讯作者: Keller，Christoph A.

Deforming symmetric product orbifolds: a tale of moduli and higher spin currents

变形对称积轨道：模量和更高自旋电流的故事

• DOI: 10.1007/jhep08(2022)159
• 发表时间: 2022
• 期刊: Journal of High Energy Physics
• 影响因子: 5.4
• 作者: Apolo, Luis;Belin, Alexandre;Bintanja, Suzanne;Castro, Alejandra;Keller, Christoph A.
• 通讯作者: Keller, Christoph A.