# 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}
}
• Published 1 May 2015
• Mathematics, Physics
• arXiv: High Energy Physics - Theory
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

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## References

SHOWING 1-10 OF 17 REFERENCES

### Renormalizability of the gradient flow in the 2D O(N) non-linear sigma model

• Mathematics
• 2014
It is known that the gauge field and its composite operators evolved by the Yang--Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this

### Perturbative analysis of the gradient flow in non-abelian gauge theories

• Physics
• 2011
The gradient flow in non-abelian gauge theories on ${\mathbb{R}^4}$ is defined by a local diffusion equation that evolves the gauge field as a function of the flow time in a gauge-covariant manner.

### Gradient flow of O(N) nonlinear sigma model at large N

• Mathematics, Physics
• 2014
A bstractWe study the gradient flow equation for the O(N) nonlinear sigma model in two dimensions at large N. We parameterize solution of the field at flow time t in powers of bare fields by

### Infinite N phase transitions in continuum Wilson loop operators

• Physics
• 2006
We define smoothed Wilson loop operators on a four dimensional lattice and check numerically that they have a finite and nontrivial continuum limit. The continuum operators maintain their character

### Trivializing Maps, the Wilson Flow and the HMC Algorithm

In lattice gauge theory, there exist field transformations that map the theory to the trivial one, where the basic field variables are completely decoupled from one another. Such maps can be

### Generalized gradient flow equation and its application to super Yang-Mills theory

• Mathematics
• 2014
A bstractWe generalize the gradient flow equation for field theories with nonlinearly realized symmetry. Applying the formalism to super Yang-Mills theory, we construct a supersymmetric extension of

### Erratum: Properties and uses of the Wilson flow in lattice QCD

Secondly, it turns out that the values of t0/a 2 quoted in the last column of table 1 are slightly wrong. The table with the corrected entries is reproduced below. While the sign error in eq. (2.25)

• 094
• 2014

• 051
• 2011