Schrödinger functional boundary conditions and improvement of the SU($N$) pure gauge action for $N>3$

Abstract

The leading method to study the running coupling constant of non-abelian gauge theories is based on the Schrödinger functional scheme. However, the boundary conditions and $\mathcal{O}(a)$ improvement have not been systematically generalized for theories with more than three colors. These theories have applications in BSM model building as well as in the large $N$ limit. We have studied the boundary conditions and improvement for the pure Yang-Mills theory within the Schrödinger functional scheme. We have determined for all values of $N$ the boundary fields which provide high signal/noise ratio. Additionally, we have calculated the improvement coefficient $c_t$ for the pure gauge to one loop order for SU($N$) gauge theories with $N=2,\dots ,8$ from which $N\ge 4$ are previously unknown.

Comments: 7 pages, 4 figures, Proceedings of the 31st International Symposium on Lattice Field Theory, July 29 - August 3, 2013, Mainz, Germany