English

Geometries from field theories

High Energy Physics - Theory 2016-06-21 v4 High Energy Physics - Lattice

Abstract

We propose a method to define a d+1d+1 dimensional geometry from a dd dimensional quantum field theory in the 1/N1/N expansion. We first construct a d+1d+1 dimensional field theory from the dd dimensional one via the gradient flow equation, whose flow time tt represents the energy scale of the system such that t0t\rightarrow 0 corresponds to the ultra-violet (UV) while tt\rightarrow\infty to the infra-red (IR). We then define the induced metric from d+1d+1 dimensional field operators. We show that the metric defined in this way becomes classical in the large NN limit, in a sense that quantum fluctuations of the metric are suppressed as 1/N1/N due to the large NN factorization property. As a concrete example, we apply our method to the O(N) non-linear σ\sigma 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.

Keywords

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

R2 v1 2026-06-22T09:26:31.513Z