Continuum limit, dynamics and holography in quantum gravity

“空间和时间的本质是什么？”几个世纪以来，这个问题一直推动着物理学的发展。物理学在20世纪初因两种不同的范式转变而发生了革命性的变化：一方面，爱因斯坦将空间和时间视为描述引力的统一的动态对象；另一方面，量子理论的发明规定了基本物质固有的模糊性。 到了20世纪末，事情变得很清楚，这两个理论分别预测了它们自己的灭亡：爱因斯坦的引力理论预测了物质向黑洞塌缩，越来越多的物质撞向时空奇点。描述基本物质相互作用的量子理论导致无限大，因此在很小的距离内就会出现不一致。因此，我们需要一个量子引力理论，用一个真正的量子时空来取代20世纪物理学所基于的平稳时空。随着时空本身成为一个模糊的对象，这样的理论将再次彻底改变我们对空间和时间的理解。 目前，我们有许多方法来研究量子引力理论，但它们都面临着一个关键的挑战：证明量子时空确实导致了平稳的时空，就像我们在日常世界中所经历的那样。只有到那时，我们才能接受一种给定的方法作为量子引力理论。这将是这个研究计划要解决的主要问题。 这是一项非常困难的任务，因为它需要跨越前所未有的数量。它可以比作从氢原子和氧原子之间的相互作用得出水的流体力学。然而，已经有了一些令人兴奋的发展，使这项任务得以实现。最重要的是，这些让我开发了一个适用于非微扰量子重力方法的重整化框架，这导致了第一个处理连续统极限的数值算法的构建。这项研究计划将扩展目前的分析和数值工具，并使用这些工具来提取量子引力模型的连续极限。 这项研究将极大地促进我们对量子引力模型中所编码的动力学的理解。不是专注于建立特定的量子引力模型，将开发的方法将允许统一处理和推导普遍预测以及依赖于模型的预测。 这将是推导物理预测和构建改进模型的关键，这将有助于我们解开量子时空的概念。 量子引力研究吸引了优秀的学生，并为推广工作提供了令人兴奋的材料。这将增加选择STEM科目的学生，并保持他们的积极性，这反过来将有助于加拿大保持和扩大其在研发领域的优势。

“What is the nature of space and time?” This is a question that has advanced the development of physics through the centuries. Physics was revolutionized at the beginning of the 20th century by two separate paradigm shifts: On the one hand, Einstein's vision of space and time as a unified and dynamical object that describes the gravitational force; on the other, the invention of quantum theory that prescribes an inherent fuzziness to fundamental matter. By the end of the 20th century, it became clear that both theories, taken separately, predict their own demise: Einstein's theory of gravitation predicts the collapse of matter to black holes, that crash more and more matter into a spacetime singularity. Quantum theory, describing the fundamental matter interactions, leads to infinities and therefore inconsistencies at very small distances. We need therefore a theory of quantum gravity that replaces smooth space time, on which 20th century physics is based, with a truly quantum space time. With space time itself becoming a fuzzy object, such a theory will again revolutionize our understanding of space and time. Currently, we have a number of approaches to a quantum theory of gravity, but they all face a key challenge: to show that quantum space time does lead to smooth space time, as we experience it in our everyday world. Only then can we accept a given approach as a theory of quantum gravity. This will be the main issue tackled by this research program. It is a very difficult task as it requires the bridging of an unprecedented number of magnitudes. It can be compared to deriving the hydrodynamics of water from the interactions between the hydrogen and oxygen atoms. There have been, however, a number of exciting developments which bring this task into reach. Most importantly, these allowed me to develop a framework of renormalization, applicable to non-perturbative quantum gravity approaches, which led to the construction of first numerical algorithms to tackle the continuum limit. This research program will expand the current analytical and numerical tools and use these to extract the continuum limit of quantum gravity models. This research will significantly advance our grasp on the dynamics encoded in quantum gravity models. Instead of being focussed on building particular models of quantum gravity, the methods that will be developed will allow a unified treatment and the derivation of universal as well as model dependent predictions. This will be key to derive physical predictions and to construct improved models, which will help us to unravel the notion of quantum space time. Quantum gravity research attracts excellent students and provides outreach efforts with exciting material. This will increase students choosing STEM subjects and keeps them motivated, which will, in turn help Canada to keep and expand its edge in the research and development sector.