The twisted gradient flow coupling at one loop

  • Eduardo I. Bribián
  • Margarita García PérezEmail author
Open Access
Regular Article - Theoretical Physics


We compute the one-loop running of the SU(N) ’t Hooft coupof twelve-flavor SU(3) gauge theoryling in a finite volume gradient flow scheme using twisted boundary conditions. The coupling is defined in terms of the energy density of the gradient flow fields at a scale \( \tilde{l} \) given by an adequate combination of the torus size and the rank of the gauge group, and is computed in the continuum using dimensional regularization. We present the strategy to regulate the divergences for a generic twist tensor, and determine the matching to the \( \overline{\mathrm{MS}} \) scheme at one-loop order. For the particular case in which the twist tensor is non-trivial in a single plane, we evaluate the matching coefficient numerically and determine the ratio of Λ parameters between the two schemes. We analyze the N dependence of the results and the possible implications for non-commutative gauge theories and volume independence.


1/N Expansion Lattice Quantum Field Theory Lattice QCD 


Open Access

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Authors and Affiliations

  • Eduardo I. Bribián
    • 1
  • Margarita García Pérez
    • 1
    Email author
  1. 1.Instituto de Física Teórica UAM-CSICUniversidad Autónoma de MadridMadridSpain

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