Monte Carlo simulations of center vortex effective models

Abstract

In this work we analyze the effective model obtained in ref. [58] via Monte Carlo techniques. In that reference, the authors consider an ensemble of closed line-like objects that obey an action that has length, curvature and contact interaction terms. After a number of controlled approximations and putting the model on a lattice, they translated averages of this confinement order parameter into the ratio between the partition function of a frustrated XY -model and its unfrustrated counterpart. Here, we shall numerically analyze different possibilities for the frustration distribution: one localized at the links that pierce the Wilson loop minimal area and one that relies on the solid angle picture, that explores the ultivaluedness of this quantity as one goes around the Wilson loop. In particular, we perform averages near the critical temperature as the continuum limit is reproduced when the system is near that point. Two results of ref. [58] were reproduced numerically: the area law near the critical temperature and the expected dependence of the string tension on the representation of the gauge group. It is also found that the N-ality 1 representations obey the constant ratio sigma N/A (1)/ sin [elevado a] 2 (pi/N) aproximadamente igual 2.038 10 [elevado a] -4 for a 11 [elevado a] 3 lattice and evidence that an area law arises from the solid angle picture