Lattice instanton action from 3D SU(2) Georgi-Glashow model

3D Georgi-Glashow model is studied on the lattice in the London limit in an infrared but an intermediate region before the screening appears. Abelian and instanton dominances are observed after abelian projections in a unitary gauge and roughly in the maximally abelian gauge. Using an inverse Monte-Carlo method, we determine an effective instanton action in both gauges. When we restrict ourselves to some regions of parameters $\beta$ and $\kappa$, we obtain an almost perfect instanton action, performing a block-spin transformation on the dual lattice. It takes a form of a Coulomb gas and reproduces fairly well the string tension obtained analytically by Polyakov. The almost perfect actions in both gauges look the same in the infrared region, which suggests gauge independence.Comment: 26 pages, 16 figure

3次元Georgi-Glashowモデルにおける格子インスタントン作用

取得学位：博士(理学)，学位授与番号：博甲第428号，学位授与年月日：平成13年3月31日,学位授与年：200

Effective Monopole Action at Finite Temperature in SU(2) Gluodynamics

Effective monopole action at finite temperature in SU(2) gluodynamics is studied on anisotropic lattices. Using an inverse Monte-Carlo method and the blockspin transformation for space directions, we determine 4-dimensional effective monopole action at finite temperature. We get an almost perfect action in the continuum limit under the assumption that the action is composed of two-point interactions alone. It depends on a physical scale $b_s$ and the temperature $T$. The temperature-dependence appears with respect to the spacelike monopole couplings in the deconfinement phase, whereas the timelike monopole couplings do not show any appreciable temperature-dependence. The dimensional reduction of the 4-dimensional SU(2) gluodynamics ((SU(2))$_{4D}$) at high temperature is the 3-dimensional Georgi-Glashow model ($(GG)_{3D}$). The latter is studied at the parameter region obtained from the dimensional red uction. We compare the effective instanton action of $(GG)_{3D}$ with the timelike monopole action obtained from (SU(2))$_{4D}$. We find that both agree very well for $T \ge 2.4T_c$ at large $b$ region. The dimensional reduction works well also for the effective action.Comment: 34 pages, 23 figure