A lattice simulation of the SU(2) vacuum structure

Abstract

In this article we analyze the vacuum structure of pure SU(2) Yang-Mills using non-perturbative techniques. Monte Carlo simulations are performed for the lattice gauge theory with external sources to obtain the effective potential.Evidence from the lattice gauge theory indicating the presence of the unstable mode in the effective potential is reported.

Monte Carlo Simulations of the SU(2) vacuum structure

“…Our data [2] show that there is no sign of the unstable mode away from the critical β region (β = 2.1 − 2.5). The situation changes dramatically in the critical region where the instability appears as a decrease of the vacuum energy contribution to the plaquette in the z direction.…”

“…We use a heat bath updating procedure with periodic boundary conditions and for the computational technique we address to reference [2]. To eliminate the homogeneous mode m = 0 we force the Polyakov line in the z direction to take a fixed value different from zero.…”

“…which is proportional to the main contribution of the vacuum energy of the plaquette in the z direction [2,3], and is very sensible to the presence of the unstable mode. The total vacuum energy obviously has also contributions from the other oriented plaquette; however, in the region we are interested, these other contributions are smoothly variable functions, and thus they will not affect the critical behavior.…”

“…In addition, several Monte Carlo simulations have already been done with a wild range of techniques in 3 and 4 Dimensions [2,3]. * Work supported in part by the U.S. Department of Energy (DOE) under contracts DE-AC02-76ER03069 and DE-FG02-91ER40676…”

Abelian chromomagnetic fields and confinement

“…(3) is invariant for gauge transformations of the external links U ext k . Different approaches to put background fields on the lattice use external currents [28][29][30][31][32][33] or modified boundary conditions [34][35][36].…”