Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1999-11-26
Nucl.Phys.B577:263-278,2000
Physics
High Energy Physics
High Energy Physics - Lattice
18 pages with 9 eps figures psfig.sty, typos corrected
Scientific paper
10.1016/S0550-3213(00)00145-0
We investigate the renormalization group (RG) flow of SU(3) lattice gauge theory in a two coupling space with couplings $\beta_{11}$ and $\beta_{12}$ corresponding to $1\times 1$ and $1\times 2$ loops respectively. Extensive numerical calculations of the RG flow are made in the fourth quadrant of this coupling space, i.e., $\beta_{11}>0$ and $\beta_{12}<0$. Swendsen's factor two blocking and the Schwinger-Dyson method are used to find an effective action for the blocked gauge field. The resulting renormalization group flow runs quickly towards an attractive stream which has an approximate line shape. This is numerical evidence of a renormalized trajectory which locates close to the two coupling space. A model flow equation which incorporates a marginal coupling (asymptotic scaling term), an irrelevant coupling and a non-perturbative attraction towards the strong coupling limit reproduces qualitatively the observed features. We further examine the scaling properties of an action which is closer to the attractive stream than the currently used improved actions. It is found that this action shows excellent restoration of rotational symmetry even for coarse lattices with $a \sim 0.3$ fm.
Forcrand Ph de
Hashimoto Tsutomu
Hioki Shinji
Matsufuru Hideo
Miyamura Osamu
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