Strong-coupling analysis of the critical dimensionality of space-time in SU(2) lattice gauge theory

Using high-order strong-coupling developments we have analyzed the phase structure of the SU(2) lattice gauge theory at different space-time dimensionalities, considering the action defined through different representations of the SU(2) group. For the Wilson action, the strong-coupling analysis is able to determine unambiguously the five-dimensional first-order phase transition. We have observed also the persistence of this first-order phase transition at higher dimensions. Strong-coupling methods have been shown to be a valuable instrument to study the behavior at high dimensionalities. In respect to the other group representations, phase transitions of first order are clearly detected for all dimensionalities higher than four. In these cases, the most difficult point is the determination of the critical dimensionality above which phase transitions are present. Only for the spin-2 representation action does a first-order phase transition at three dimensions seem to be present. © 1987 The American Physical Society.