Fixed point actions in SU(3) gauge theory: surface tension and topology

Lattice actions living on the direction of the space of couplings which originates at the fixed point of a renormalization group (RG) transformation and leaves orthogonally the critical surface, are called fixed point (FP) actions. They are classical perfect actions and have many interesting properties [1]. In particular, FP actions possess scale-invariant instanton solutions. Given a RG transformation, the FP action of any lattice configuration is well defined and can be determined numerically by multigrid minimization [2]. In Monte Carlo simulations, however, only simple enough parametrizations of the FP action can be used. In Sect. 2 the so called “type III” parametrized FP action proposed in Ref. [3] is used to study some typical observables in SU(3) thermodynamics at high temperatures (free energy density) and at criticality (surface tension). In Sect. 3 a new, approximately scale-invariant parametrization of the FP action is proposed to be used in SU(3) topology.