Research of Lattice Field Theory with rheta-Term by Renormalization Group

重正化群的带变项的格场论研究

基本信息

批准号：
08640381
负责人：
IMACHI Masahiro
金额：
$ 1.34万
依托单位：
YAMAGATA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1997
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08640381/
关键词：
U (N) gauge theory topological term rheta parameter renormalization group non Abelian gauge theory CP^<N-1> field theory oblique confinement duality データパラメータ CPN場理論 θ項トポロジカル荷電固定点相構造とじこめ虚作用 renormalized trajectory

项目摘要

On the basis of the previous research on U (1) gauge theory, we investigated U (2) lattice gauge theory with rheta-term in 2 dimensions by renormalization group.The reason to choose the group U(2) is that we are interested in the role of non Abelian part. The simplest among such group is U (2), so we began the study on this gauge group. The action is given by non Abelian real part and Abelian imaginary part in 2 dimensions. In contrast to 4 dimensional theory, we can not construct non Abelian imaginary part. This is because the topological term is given by iTrepsilon_<munu>F_<munu> in 2 dimensions, and it gives zero when we choose SU (2) (non Abelian) part.As a bare action, we adopt 1) real action ; defined by couplings, betal_1l_2=beta_<11> (l_1=4q, l_2=2I) * 0, (q means U (1) charge, and I means SU (2) isotopic spin), 2) imaginary action ; standard rheta action (i (rheta/2pi) Trepsilon_<munu>F_<munu>. This is defined by U (1) part.).After renomalization transformations, there appears non Abelian part in imaginary action, it, however, converges to zero after many renomalization group transformations.Phase transition occurs only when rheta=pi and in the irreducible representation which is trivial in SU (2), i.e., for ( (l_1, l_2) = (2,0), namely, the representation with q=1, I=0), but not in non trivial SU (2) representation ( (l_1, l_2) = (1,1), namely, q=1/2, I=1/2). This is due to the SU (2) confinement mechanism which forbids deconfinement transition even at rheta=pi.Real action approaches "heat kernel" type by renormalization group transformations. We are performing also 1) 4 dimensional Z_N theory with rheta-term, which is interesting because it is related with "duality" and "oblique confinement" (Imachi, Liu and Yoneyama), 2) numerical study of CP^<N-1> with N lager than 2 (Imachi, Kanou and Yoneyama).

基于先前关于U（1）量规理论的研究，我们研究了U（2）晶格计理论，其rheta-term在重新归一化组中具有2个维度。选择u（2）的理由是我们感兴趣的是我们感兴趣的。在非亚伯利亚部分的角色中。在此类组中，最简单的是u（2），因此我们开始了该量规组的研究。该动作是由非阿贝里安真实部分和阿贝尔假想部分在两个维度中给出的。与4维理论相反，我们无法构建非亚伯假想部分。这是因为拓扑术语由itrepsilon_ <munu> f_ <munu>在2个维度中给出，并且当我们选择su（2）（2）（非Abelian）部分时，它给出了零。由耦合定义，betal_1l_2 = beta_ <11>（l_1 = 4q，l_2 = 2i） * 0，（q表示U（1）电荷，我的意思是SU（2）同位素旋转），2）假想动作；标准rheta动作（i（rheta/2pi）trepsilon_ <munu> f_ <munu>。这是由u（1）部分定义的。在许多肾化组转换之后，零是零，仅在rheta = pi和不可减至的表示中发生，而在su（2）中是微不足道的（即（（l_1，l_2）=（2,2,0）， q = 1，i = 0），但在非琐事su（2）表示（（l_1，l_2）=（1,1），即q = 1/2，i = 1/2）中不进行。这是由于SU（2）限制机制，该机制即使在rheta = pi.Real动作接近“热内核”类型的情况下，该机制也禁止解糊化过渡。我们还执行1）4维Z_n理论，具有rheta-enmer，这很有趣，因为它与“二元性”和“倾斜限制”（Imachi，liu and yoneyama），2）CP^<n-1的数值研究> n lager超过2（Imachi，Kanou和Yoneyama）。