Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-08-11
JHEP 0610:042,2006
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, 23 figures, references added
Scientific paper
10.1088/1126-6708/2006/10/042
Recent perturbative studies show that in 4d non-commutative spaces, the trivial (classically stable) vacuum of gauge theories becomes unstable at the quantum level, unless one introduces sufficiently many fermionic degrees of freedom. This is due to a negative IR-singular term in the one-loop effective potential, which appears as a result of the UV/IR mixing. We study such a system non-perturbatively in the case of pure U(1) gauge theory in four dimensions, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d=2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non-commutativity parameter $\theta$, which provides evidence for a possible continuum theory. The extent of the dynamically generated space in the non-commutative directions becomes finite in the above limit, and its dependence on $\theta$ is evaluated explicitly. We also study the dispersion relation. In the weak coupling symmetric phase, it involves a negative IR-singular term, which is responsible for the observed phase transition. In the broken phase, it reveals the existence of the Nambu-Goldstone mode associated with the spontaneous symmetry breaking.
Bietenholz Wolfgang
Nishimura Jun
Susaki Yoshiaki
Volkholz Jan
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