Improving the continuum limit of gradient flow step scaling

  • Anqi Cheng
  • Anna Hasenfratz
  • Yuzhi Liu
  • Gregory Petropoulos
  • David Schaich
Open Access


We introduce a non-perturbative improvement for the renormalization group step scaling function based on the gradient flow running coupling, which may be applied to any lattice gauge theory of interest. Considering first SU(3) gauge theory with N f = 4 massless staggered fermions, we demonstrate that this improvement can remove \( \mathcal{O}\left( {{a^2}} \right) \) lattice artifacts, and thereby increases our control over the continuum extrapolation. Turning to the 12-flavor system, we observe an infrared fixed point in the infinite-volume continuum limit. Applying our proposed improvement reinforces this conclusion by removing all observable \( \mathcal{O}\left( {{a^2}} \right) \) effects. For the finite-volume gradient flow renormalization scheme defined by \( c={{{\sqrt{8t }}} \left/ {L=0.2 } \right.} \), we find the continuum conformal fixed point to be located at \( g_{\star}^2=6.2(2) \).


Renormalization Group Lattice Quantum Field Theory 


Open Access

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Anqi Cheng
    • 1
  • Anna Hasenfratz
    • 1
  • Yuzhi Liu
    • 1
  • Gregory Petropoulos
    • 1
  • David Schaich
    • 1
    • 2
  1. 1.Department of PhysicsUniversity of ColoradoBoulderUnited States
  2. 2.Department of PhysicsSyracuse UniversitySyracuseUnited States

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