### Abstract

The Yang-Mills gradient flow is considered on the four dimensional torus T4 for SU(N) gauge theory coupled to Nf flavors of massless fermions in arbitrary representations. The small volume dynamics is dominated by the constant gauge fields. The expectation value of the field strength tensor squared TrFμνFμν(t) is calculated for positive flow time t by treating the non-zero gauge modes perturbatively and the zero modes exactly. The finite volume correction to the infinite volume result is found to contain both algebraic and exponential terms. The leading order result is then used to define a one parameter family of running coupling schemes in which the coupling runs with the linear size of the box. The new scheme is tested numerically in SU(3) gauge theory coupled to Nf = 4 flavors of massless fundamental fermions. The calculations are performed at several lattice spacings with a controlled continuum extrapolation. The continuum result agrees with the perturbative prediction for small renormalized coupling as expected.

Original language | English |
---|---|

Article number | 007 |

Journal | Journal of High Energy Physics |

Volume | 2012 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2012 |

### Fingerprint

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2012*(11), [007]. https://doi.org/10.1007/JHEP11(2012)007

**The Yang-Mills gradient flow in finite volume.** / Fodor, Z.; Holland, Kieran; Kuti, Julius; Nogradi, Daniel; Wong, Chik Him.

Research output: Article

*Journal of High Energy Physics*, vol. 2012, no. 11, 007. https://doi.org/10.1007/JHEP11(2012)007

}

TY - JOUR

T1 - The Yang-Mills gradient flow in finite volume

AU - Fodor, Z.

AU - Holland, Kieran

AU - Kuti, Julius

AU - Nogradi, Daniel

AU - Wong, Chik Him

PY - 2012

Y1 - 2012

N2 - The Yang-Mills gradient flow is considered on the four dimensional torus T4 for SU(N) gauge theory coupled to Nf flavors of massless fermions in arbitrary representations. The small volume dynamics is dominated by the constant gauge fields. The expectation value of the field strength tensor squared TrFμνFμν(t) is calculated for positive flow time t by treating the non-zero gauge modes perturbatively and the zero modes exactly. The finite volume correction to the infinite volume result is found to contain both algebraic and exponential terms. The leading order result is then used to define a one parameter family of running coupling schemes in which the coupling runs with the linear size of the box. The new scheme is tested numerically in SU(3) gauge theory coupled to Nf = 4 flavors of massless fundamental fermions. The calculations are performed at several lattice spacings with a controlled continuum extrapolation. The continuum result agrees with the perturbative prediction for small renormalized coupling as expected.

AB - The Yang-Mills gradient flow is considered on the four dimensional torus T4 for SU(N) gauge theory coupled to Nf flavors of massless fermions in arbitrary representations. The small volume dynamics is dominated by the constant gauge fields. The expectation value of the field strength tensor squared TrFμνFμν(t) is calculated for positive flow time t by treating the non-zero gauge modes perturbatively and the zero modes exactly. The finite volume correction to the infinite volume result is found to contain both algebraic and exponential terms. The leading order result is then used to define a one parameter family of running coupling schemes in which the coupling runs with the linear size of the box. The new scheme is tested numerically in SU(3) gauge theory coupled to Nf = 4 flavors of massless fundamental fermions. The calculations are performed at several lattice spacings with a controlled continuum extrapolation. The continuum result agrees with the perturbative prediction for small renormalized coupling as expected.

KW - Lattice Gauge Field Theories

KW - Lattice Quantum Field Theory

UR - http://www.scopus.com/inward/record.url?scp=84869055318&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869055318&partnerID=8YFLogxK

U2 - 10.1007/JHEP11(2012)007

DO - 10.1007/JHEP11(2012)007

M3 - Article

AN - SCOPUS:84869055318

VL - 2012

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 11

M1 - 007

ER -