Abstract:
This thesis makes a systematic study of the SO(3) Lattice Gauge Theory at finite temperature. The study of the SO(3) Lattice Gauge Theory is important in understanding the implications of lattice gauge theories for the high temperature phase of the SU(2) Yang-Mills theory. The existence of a first order bulk transition at zero temperature that can influence its finite temperature behaviour, and the presence of a local symmetry which requires the usage of a different set of observables to study its property - are some of the complications present in the study of SO(3) theory. The Wilson-Polyakov line in the adjoint representation of SU(2) is mainly used to make the present study. The role of Z(2) monopoles in determining the various phases is considered. The adjoint Wilson line displays an unusual behaviour at low and high temperature is found, whereas the fundamental Wilson line is always zero in this model. The high temperature phase of the theory is analyzed by looking at single site histograms for the fundamental and adjoint Wilson lines, and interpreted for comparisons with the high temperature phase. It is shown that the high temperature phase of SO(3) LGT is like the deconfined phase of the SU(2) LGT theory, but unlike the breaking of any symmetry as in SU(2) theory. An interference of the bulk transition in the finite temperature theory is observed. The evidence for a new phase transition, within the relevance region with respect to continuum theory is presented; The conjectures phase diagram for the SO(3) LGT theory at finite temperature is presented, and contrasted with that of SU(2) LGT. The implications of the study results for the high temperature phase of the SU(2) Yang-Mills theory is discussed with the argument that it is in the Higgs Phase.
