Vortices in the SU(N) x SU(N) spin systems in two dimensions

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1982

OSTI ID:6236294

Kares, R J.D.

The SU(N) x SU(N) or chiral spin systems in two dimensions with spin variables in both the fundamental and the adjoint representations of SU(N) are considered. In the adjoint representation the chiral models are found to possess topologically stable, classical vortex solutions which carry a Z(N) topological charge. A relationship is established between the chiral models and massive Yang-Mills theory in two dimensions. This relationship is exploited to prove the asymptotic freedom of the chiral models and to find their weak coupling mass gap. The connection between the vortices of the chiral models and those of the massive Yang-Mills theory is discussed. The behavior of a gas of vortices in the SU(2) chiral model is considered. This gas is converted to an equivalent field theory and studied using the renormalization group. It is shown that the SU(2) vortex gas does not undergo a Kosterlitz-Thouless phase transition. This behavior probably persists for the higher SU(N) groups as well. Finally, using the massive Yang-Mills theory the effect of the coupling of vortices to spin wave fluctuations is investigated. It is argued that as a result of the vortex-spin wave interaction the vortices acquire a mass scale dynamically. A self consistency condition is derived for the vortex scale and used to compute the mass gap for the chiral models in the presence of vortices. The mass gap obtained in this way is found to be in agreement with the weak coupling result suggesting that vortices may be responsible for generating the mass gap in the chiral models near T = 0.

• Research Organization: California Univ., Irvine (USA)
• OSTI ID: 6236294
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
CHIRALITY
FLUCTUATIONS
LIE GROUPS
MATHEMATICAL MODELS
NUCLEAR MODELS
PARTICLE PROPERTIES
PHASE TRANSFORMATIONS
SPIN
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS
TWO-DIMENSIONAL CALCULATIONS
VARIATIONS
VORTICES
WEAK-COUPLING MODEL
YANG-MILLS THEORY