Abstract
SU(2) gauge theory is investigated with a lattice action which is insensitive to small perturbations of the lattice gauge fields. Bare perturbation theory can not be defined for such actions at all. We compare non-perturbative continuum results with that obtained by the usual Wilson plaquette action. The compared observables span a wide range of interesting phenomena: zero temperature large volume behavior (topological susceptibility), finite temperature phase transition (critical exponents and critical temperature) and also the small volume regime (discrete β-function or step-scaling function). In the continuum limit perfect agreement is found indicating that universality holds for these topological lattice actions as well.
Highlights
We investigate the same phenomenon for non-abelian gauge theories
In the continuum limit perfect agreement is found indicating that universality holds for these topological lattice actions as well
We show that for SU(2) pure gauge theory the non-perturbative continuum results obtained with the topological action agree with that of the usual Wilson plaquette action which we know is in the correct universality class of Yang-Mills theory
Summary
We seek an action which is gauge invariant. The simplest possibility is to use the usual plaquette P as the only building block,. Gauge invariance is encoded in a gauge invariant definition of the boundary between allowed and not allowed links It is well-known [7] that if the plaquettes on a lattice are all restricted to be very small,. In all runs with the topological action we use a simple Metropolis algorithm whereas with the Wilson plaquette action a heat bath algorithm Both Metropolis and heat bath sweeps are accompanied by two to five overrelaxation steps [9]. An allowed configuration by the topological action may turn into a forbidden configuration by an overrelaxation step, in this case the step is rejected and the original configuration is kept
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