Scattering in Quantum Gravity: Symmetries and Holography

该奖项资助纽约大学Monica Pate教授的研究活动。统一量子力学和引力的完整理论的表述仍然是现代物理学前沿的一个基本开放问题。量子引力的主题不仅对我们对自然世界的理解具有重要意义，而且还提出了独特的挑战，推动了对全新物理原理的探索。值得注意的是，一种被称为全息术的新原理已经成为一种潜在的解决方案。目前，全息原理是一种假设，即量子引力系统在更小的维度上等同于没有引力的普通物理系统。这个想法类似于全息投影中的每个细节如何被精确地捕捉到相应的全息板上。虽然量子引力有意义的进展已经从全息原理的具体实现中出现，但这个主题的许多基本方面仍未得到解决。值得注意的是，我们对假设的粒子对撞机缺乏明确的预测，这种对撞机足够强大，可以在量子水平上探测引力。Pate教授的研究旨在通过专门定制全息原理的新扩展来解决量子引力散射问题，从而弥合这一差距。通过这项研究，佩特教授的努力将有助于实现对自然世界的精确技术理解的国家利益。这项工作将批判性地评估全息术作为描述量子引力所必需的新物理范式的可行性，同时也为更基本的问题提供有价值的见解，包括那些关于宇宙基本构建块的身份的问题。虽然佩特教授的研究内容是根据智力价值来选择的，但与基于方法的项目相比，问题驱动型项目的战略选择非常适合于让新人才更容易进入一个技术强大的领域。在这些项目过程中提供的指导将有助于培养新的科学领袖，并有助于妇女和其他代表性不足的群体成员充分参与高能理论领域的持续增长。因此，这些努力构成了创建一个公平和多样化的科学界的更广泛努力的一部分。在更技术性的层面上，Pate教授的研究旨在限制和确定量子引力中的散射振幅。分析将需要将全息原理从已经得到充分研究的渐近反德西特时空的背景扩展到渐近平坦时空，这是引力散射问题最自然的背景。更具体地说，将研究天体全息方案的各个方面，该方案假定引力散射与天球上的共形对称理论之间的等价。一个主要目标是在类似于现实世界的量子引力系统的背景下发展和评估天体全息术的可行性。一个特定的目标是将许多新的对称性和类似的组织原理扩展到天体全息学的最新进展中，以大规模散射粒子。另一个重点将是在天体全息术中发展边界和体重正化的连贯图像。方法将包括自上而下和自下而上方法的综合。一个辅助目标是在已知的物理定律范围内发现新的现象。对最近发现的渐近平坦时空的对称性的发现和利用将是沿着这条战线取得进展的主要方法。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award funds the research activities of Professor Monica Pate at New York University.The formulation of a complete theory unifying quantum mechanics and gravity remains a fundamental open problem at the forefront of modern physics. The subject of quantum gravity not only holds great significance for our understanding of the natural world, but also presents unique challenges that drive a quest for entirely new principles of physics. Remarkably, a new principle known as holography has emerged as a potential solution. At present, the holographic principle is the conjecture that systems of quantum gravity are equivalent to ordinary physical systems without gravity in fewer dimensions. This idea is similar to how every detail in a holographic projection is precisely captured on the corresponding holographic plate. While meaningful progress in quantum gravity has arisen from concrete realizations of the holographic principle, many fundamental aspects of the subject remain unresolved. Notably, we lack definitive predictions for a hypothetical particle collider that is powerful enough to probe the gravitational force at the quantum level. Professor Pate's research aims to bridge this gap by specifically tailoring a novel extension of the holographic principle to this quantum gravitational scattering problem. Through this research, Professor Pate's endeavors will contribute to the national interest in attaining a precise technical understanding of the natural world. This work will critically evaluate the viability of holography as the new physical paradigm necessary for describing quantum gravity, while also providing valuable insight into more basic questions including those regarding the identity of the fundamental building blocks of the universe. While the content of Professor Pate's research is selected based on intellectual merit, the strategic choice of problem-driven as opposed to methods-based projects is well-suited for easing the entry of new talent into a technically formidable field. The mentorship provided during the course of these projects will contribute to the development of new scientific leaders as well as to a sustained growth towards the full participation of women and members of other underrepresented groups in the field of high energy theory. As such, these efforts form part of the broader endeavor to create an equitable and diverse scientific community.At a more technical level, Professor Pate's research aims to constrain and determine scattering amplitudes in quantum gravity. Analyses will entail an extension of the holographic principle from the well-studied context of asymptotically Anti-de Sitter spacetimes to asymptotically flat spacetimes, which are the most natural setting for the gravitational scattering problem. More specifically, aspects of the celestial holographic proposal, which posits an equivalence between gravitational scattering and a theory with conformal symmetry on the celestial sphere, will be investigated. A primary objective is to develop and assess the viability of celestial holography in the context of quantum gravitational systems that resemble the real world. A specific goal is to extend many of the novel symmetries and similar organizing principles underlying recent progress in celestial holography to massive scattering particles. Another focus will be to develop a coherent picture of boundary and bulk renormalization in celestial holography. Methods will include a synthesis of top-down and bottom-up approaches. An auxiliary objective is to uncover new phenomena within the known laws of physics. The discovery and exploitation of recently-discovered symmetries of asymptotically flat spacetimes is the main approach that will be employed to make progress along this front.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.