Geometries from field theories

@article{Aoki2015GeometriesFF,
  title={Geometries from field theories},
  author={Sinya Aoki and Kengo Kikuchi and Tetsuya Onogi},
  journal={arXiv: High Energy Physics - Theory},
  year={2015}
}
We propose a method to define a $d+1$ dimensional geometry from a $d$ dimensional quantum field theory in the $1/N$ expansion. We first construct a $d+1$ dimensional field theory from the $d$ dimensional one via the gradient flow equation, whose flow time $t$ represents the energy scale of the system such that $t\rightarrow 0$ corresponds to the ultra-violet (UV) while $t\rightarrow\infty$ to the infra-red (IR). We then define the induced metric from $d+1$ dimensional field operators. We show… 

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