Computational Approach to Quantum Gravity via Holography

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.