Geometries from field theories
Abstract
We propose a method to define a dimensional geometry from a dimensional quantum field theory in the expansion. We first construct a dimensional field theory from the dimensional one via the gradient flow equation, whose flow time represents the energy scale of the system such that corresponds to the ultra-violet (UV) while to the infra-red (IR). We then define the induced metric from dimensional field operators. We show that the metric defined in this way becomes classical in the large limit, in a sense that quantum fluctuations of the metric are suppressed as due to the large factorization property. As a concrete example, we apply our method to the O(N) non-linear model in two dimensions. We calculate the three dimensional induced metric, which is shown to describe an AdS space in the massless limit. We finally discuss several open issues in future studies.
Cite
@article{arxiv.1505.00131,
title = {Geometries from field theories},
author = {Sinya Aoki and Kengo Kikuchi and Tetsuya Onogi},
journal= {arXiv preprint arXiv:1505.00131},
year = {2016}
}
Comments
9 pages, the title has been changed, and some contents have also been modified. This version is accepted for a publication in PTEP