Renormalization group flow of SU(3) lattice gauge theory : Numerical studies in a two coupling space
NuclearPhysicsB_577_263.pdf 773 KB
Ph. de Forcrand
M. García Pérez
SU(3) lattice gauge theory
Renormalization group flow
We investigate the renormalization group flow of SU(3) lattice gauge theory in two coupling space with β11 of plaquette and β12 of rectangular actions. Extensive numerical calculations of the RG flow are made in the fourth quadrant of the coupling space, i.e., β11 > 0 and β12 < 0. Swendsen's factor 2 blocking and Schwinger-Dyson method are used to find an effective action for the blocked gauge field. Resultant renormalization group flow runs quickly towards an attractive stream which has approximate line shape. This is a numerical evidence of the 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 nonperturbative attraction toward strong coupling limit reproduces qualitatively the observed feature. We further examine scaling property of an action which is closer to the attractive stream than the currently used improved actions. It is found that the action shows excellent restoration of rotational symmetry even for coarse lattices with o ~ 0.4 fm.
Nuclear Physics B
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