The Yang-Mills gradient flow in finite volume

Z. Fodor, Kieran Holland, Julius Kuti, Daniel Nogradi, Chik Him Wong

Research output: Article

71 Citations (Scopus)

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 languageEnglish
Article number007
JournalJournal of High Energy Physics
Volume2012
Issue number11
DOIs
Publication statusPublished - 2012

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gradients
gauge theory
fermions
continuums
boxes
extrapolation
field strength
spacing
tensors
predictions

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

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

In: Journal of High Energy Physics, Vol. 2012, No. 11, 007, 2012.

Research output: Article

Fodor, Z. ; Holland, Kieran ; Kuti, Julius ; Nogradi, Daniel ; Wong, Chik Him. / The Yang-Mills gradient flow in finite volume. In: Journal of High Energy Physics. 2012 ; Vol. 2012, No. 11.
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