The Yang-Mills gradient flow in finite volume

Zoltan Fodor, Kieran Holland, Julius Kuti, Daniel Nogradi, Chik Him Wong

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103 Scopus citations


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 (US)
Article number7
JournalJournal of High Energy Physics
Issue number11
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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