A group of researchers from Osaka University and Kyoto University succeeded in calculating the exact partition function of the three-dimensional (2 spatial and 1 temporal) quantum gravity theory when a cosmological constant is negative under a certain equivalence, a world first. Quantum gravity theory is a theory integrating the two main pillars of modern physics: quantum mechanics and Einstein’s general theory of relativity.

Quantum mechanics calculates the path particles, such as electrons, take. Path integral, the basic principle of quantum mechanics, was difficult to calculate with conventional methods; therefore, researchers could only rely on approximate methods. On the other hand, three-dimensional Euclidean pure gravity theory is known to be equivalent to Chern-Simons theory, classically.

This group succeeded in exactly calculating path integral (a key point in quantum theory) in Chern-Simons theory by using the recently developed localization technique. As Chern-Simons theory is thought to be formulated in terms of three-dimensional Euclidean pure gravity, it can be said that this group performed exact calculation of three-dimensional Euclidean pure gravity theory.

In order to understand questions such as “How did the universe begin before the Big Bang?” and “What is happening at the center of a black hole?” quantum gravity theory beyond the framework of a standard modern physics theory is necessary. Quantum gravity theory is a key to understanding the creation of the universe. This group’s research results are a step toward understanding quantum gravity theory currently being developed. The results will serve as a stepping stone to further understanding of quantum gravity theory, quantum field theory, and gauge/gravity duality as well.

To calculate the partition function Z of the three-dimensional quantum gravity, it is necessary to perform a path-integral of spacetimes. In this research, the exact partition function of the three-dimensional quantum gravity was calculated with use of localization, by identifying the path-“integral” of the spacetimes with a “summation” of exact solutions of Chern-Simons theory on various spacetimes.

(Link) http://resou.osaka-u.ac.jp/en/research/2015/20151023_1