Computational Approach to Quantum Gravity via Holography

STFC战略围绕着挑战性的问题而建立，例如：“宇宙是如何开始的，它是如何演化的？”，“宇宙的基本成分和结构是什么，它们是如何相互作用的？”，“时空的本质是什么？”，“是否有一个统一的框架？”这项研究方案旨在基于一种新的方法来解决这些问题，该方法结合了由STFC支持的几个不同研究领域的技术。目前对自然基本定律的理解是基于粒子物理(电磁、弱相互作用和强相互作用)和广义相对论(引力)的标准模型。这一框架远未完成。最大的问题是它不是一个统一的框架：虽然标准模型被量子力学处理，但对引力的量子方面却知之甚少。为了理解像宇宙的起源或时空的本质这样的深层问题，我们需要一个统一的框架，以量子力学的方式对待所有基本的相互作用。首先要做的是获得量子引力理论。超弦理论是一种很有前途的量子引力理论，人们希望它也能为我们提供自然界中所有基本相互作用的统一框架。我们将弦理论发展出的吸引人的想法-全息原理-与粒子论、核理论和量子信息的技术相结合，以揭示引力的量子方面。全息原理是一个非常引人注目的想法，它声称量子引力等同于某些没有引力的量子理论。非引力理论的性质可以通过一套称为全息词典的非平凡规则转化为引力的量子方面。一个直接的结果是，量子黑洞应该用明显的么正理论来描述，从而提供了霍金信息损失悖论的反例。由于全息原理，人们可能能够使用非引力理论来学习超弦理论的动力学，这些理论原则上可以用数值方法来研究和求解。然而，障碍是缺乏计算工具。通过全息字典与引力相关的非引力理论类似于量子色动力学(QCD)，这是原子内部强相互作用的理论。QCD是出了名的难以用纸笔解决。然而，在这二十年里，核理论家和格点规范理论家发展了求解QCD的数值方法，到目前为止，QCD的各种性质，如质子的质量，都可以用数值方法计算。在过去的几年里，我已经解决了与我们感兴趣的理论相关的几个技术难题，并证明了类似QCD的方法实际上可以使用。我还证明了量子引力的一些重要性质实际上可以通过数值计算获得。另一个强大的工具来自量子信息理论。对于许多有趣的问题，如霍金的信息悖论，重要的是观察量子黑洞是如何演化的。然而，这样的计算是出了名的困难。最近人们意识到，一些简单的理论捕捉了量子黑洞时间演化的许多方面，而量子信息论的工具被证明对这些理论有用。在欧内斯特·卢瑟福奖学金和南安普敦大学的帮助下，我将进一步推动这些方法，并建立一种计算量子引力的方法。它应该为物理学家提供寻找自然基本定律的统一框架的基本工具。

The STFC strategy is built around challenging questions like "How did the universe begin and how is it evolving?", "What are the fundamental constituents and fabric of the universe and how do they interact?", "What is the nature of spacetime?", "Is there a unified framework?". This research proposal aims to address these questions based on a new approach which combines techniques from several different research fields supported by STFC.Current understanding about the fundamental laws of nature is based on the standard model of particle physics (electromagnetism, weak interaction and strong interaction) and general relativity (gravity). This framework is far from complete. The biggest problem is that it is not a 'unified framework': while the standard model is treated quantum mechanically, the quantum aspect of gravity is poorly understood. In order to understand deep questions like the beginning of the universe or the nature of spacetime, we need a unified framework which treats all fundamental interactions quantum mechanically. The first thing to do is to obtain the theory of quantum gravity. Superstring theory is a promising theory of quantum gravity, and it is hoped that it also provides us with the unified framework of all fundamental interactions in nature. We combine an attractive idea developed from string theory - the holographic principle - with techniques from particle theory, nuclear theory and quantum information, in order to reveal the quantum aspects of gravity. The holographic principle is a very striking idea which claims quantum gravity is equivalent to certain quantum theories without gravity. The properties of the non-gravitational theories can be translated to quantum aspects of gravity via a set of nontrivial rules called holographic dictionary. One immediate consequence is that a quantum black hole should be described by manifestly unitary theory, thus providing a counter-example of Hawking's information loss paradox. Thanks to the holographic principle, one may be able to use non-gravitational theories, which in principle can be studied and solved numerically, to learn about the dynamics of superstring theory. The obstacle is, however, the lack of computational tools. Non-gravitational theories related to gravity via holographic dictionary resemble Quantum Chromodynamics (QCD), which is the theory of strong interaction inside the atom. QCD is notoriously difficult to solve by a pen and paper. However, in these two decades, nuclear theorists and lattice gauge theorists developed numerical methods to solve QCD, and by now various properties of QCD, for example the mass of proton, can be calculated numerically. In the past several years I have solved several technical difficulties associated with theories of our interest, and shown that QCD-like methods can actually be used. I have also demonstrated that a few important properties of quantum gravity can actually be obtained by numerical calculation. Another powerful tool comes from quantum information theory. For many interesting problems like Hawking's information paradox, it is important to see how quantum black holes evolve. However such calculations are notoriously difficult. Recently it has been realized that some simple theories capture many aspects of time evolutions of quantum black holes, and tools from quantum information theory turned out to be useful for these theories. With the Ernest Rutherford fellowship and the University of Southampton, I will push these approaches further and establish a computational approach to quantum gravity. It should provide physicists with basic tools for the search for the unified framework of the fundamental laws of nature.