Two perspectives of the 2D unit area quantum sphere and their equivalence
Probability
2017-09-12 v3 Mathematical Physics
math.MP
Abstract
2D Liouville quantum gravity (LQG) is used as a toy model for 4D quantum gravity and is the theory of world-sheet in string theory. Recently there has been growing interest in studying LQG in the realm of probability theory: David, Kupiainen, Rhodes, Vargas (2014) and Duplantier, Miller, Sheffield (2014) both provide a probabilistic perspective of the LQG on the 2D sphere. In particular, in each of them one may find a definition of the so-called unit area quantum sphere. We examine these two perspectives and prove their equivalence by showing that the respective unit area quantum spheres are the same. This is done by considering a unified limiting procedure for defining both objects.
Keywords
Cite
@article{arxiv.1512.06190,
title = {Two perspectives of the 2D unit area quantum sphere and their equivalence},
author = {Juhan Aru and Yichao Huang and Xin Sun},
journal= {arXiv preprint arXiv:1512.06190},
year = {2017}
}
Comments
minor revisions; final version