Schrödinger functional boundary conditions and improvement for N>3

Abstract

The standard method to calculate non-perturbatively the evolution of the running coupling of a SU(N) gauge theory is based on the Schrödinger functional (SF). In this paper we construct a family of boundary fields for general values of N which enter the standard definition of the SF coupling. We provide spatial boundary conditions for fermions in several representations which reduce the condition number of the squared Dirac operator. In addition, we calculate the O(a) improvement coefficients for N>3 needed to remove boundary cutoff effects from the gauge action. After this, residual cutoff effects on the step scaling function are shown to be very small even when considering non-fundamental representations. We also calculate the ratio of Lambda parameters between the MS-bar and SF schemes.

33 pages, 6 figures

References in corpus (7)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Infinite N phase transitions in continuum Wilson loop operators
• SU(N) gauge theories at large N
• Running coupling constant of ten-flavor QCD with the Schrödinger functional method
• Mass anomalous dimension in SU(2) with six fundamental fermions
• Higher representations on the lattice: perturbative studies
• Lattice artefacts in the Schrödinger Functional coupling for strongly interacting theories