# 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…

## 16 Citations

### Encoding field theories into gravities

- Physics
- 2016

We propose a method to give a $d+1$ geometry from a $d$ dimensional quantum field theory in the large N expansion. We first construct a $d+1$ dimensional field from the $d$ dimensional one using the…

### Flow equation for the scalar model in the large $N$ expansion and its applications

- Mathematics
- 2016

We study the flow equation of the O($N$) $\varphi^4$ model in $d$ dimensions at the next-to-leading order (NLO) in the $1/N$ expansion. Using the Schwinger-Dyson equation, we derive 2-pt and 4-pt…

### Flow equation of N$$ \mathcal{N} $$ = 1 supersymmetric O(N ) nonlinear sigma model in two dimensions

- Mathematics
- 2017

A bstractWe study the flow equation for the N$$ \mathcal{N} $$ = 1 supersymmetric O(N ) nonlinear sigma model in two dimensions, which cannot be given by the gradient of the action, as evident from…

### Flow equation for the large N scalar model and induced geometries

- Physics
- 2016

We study the proposal that a (d+1)-dimensional induced metric is constructed from a d-dimensional field theory using gradient flow. Applying the idea to the O(N) ϕ4 model and normalizing the flow…

### Generalized Gradient Flow Equation and Its Applications

- Mathematics, Physics
- 2015

We propose a generalization of the gradient flow equation for quantum field theories with nonlinearly realized symmetry. Applying the equation to $\mathcal{N}=1$ $SU(N)$ super Yang-Mills theory in…

### Holographic geometry for nonrelativistic systems emerging from generalized flow equations

- Physics, MathematicsPhysical Review D
- 2019

An intriguing result presented by two of the present authors is that an anti de Sitter space can be derived from a conformal field theory by considering a flow equation. A natural expectation is that…

### Results and techniques for higher order calculations within the gradient-flow formalism

- PhysicsJournal of High Energy Physics
- 2019

A bstractWe describe in detail the implementation of a systematic perturbative approach to observables in the QCD gradient-flow formalism. This includes a collection of all relevant Feynman rules of…

### Gradient flow and the Wilsonian renormalization group flow

- Physics
- 2018

The gradient flow is the evolution of fields and physical quantities along a dimensionful parameter~$t$, the flow time. We give a simple argument that relates this gradient flow and the Wilsonian…

### Holographic de Sitter spacetime and quantum corrections to the cosmological constant

- Physics
- 2020

A dynamical aspect of quantum gravity on de Sitter spacetime is investigated by holography or the dS/CFT correspondence. We show that de Sitter spacetime emerges from a free Sp(N) vector model by…

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