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

• 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

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).

在前人对U(1)规范理论研究的基础上，我们利用重整化群研究了二维含Rheta项的U(2)格点规范理论，选择U(2)群是因为我们对非阿贝尔部分的作用感兴趣。在这些群中最简单的是U(2)，所以我们开始了对这个规范群的研究。作用由二维的非阿贝尔实部和阿贝尔虚部给出。与四维理论相比，我们不能构造非阿贝尔虚部。这是因为拓扑项是由iTrepsilon；lt；munu&gt；F_&lt；munu&gt；给出的，当我们选择SU(2)(非阿贝尔)部分时，它给出了零。作为一个裸作用，我们采用1)实作用；由耦合定义，Betal_1l_2=β_&lt；11&gt；(L_1=4q，L_2=2i)*0，(Q表示U(1)电荷，I表示SU(2)同位素自旋)，2)虚作用；标准的瑞塔作用(I(Rheta/2pi)Trepsilon_&lt；munu&gt；F_&lt；munu&gt；这是由U(1)部分定义的。经过重整化变换后，虚作用中出现了非阿贝尔部分，但经过多次重整化群变换后，它收敛到零。只有当Rheta=pi时，相变才发生在SU(2)中平凡的不可约表示中，即(L_1，L_2)=(2，0)，即具有q=1，i=0的表示，但在非平凡SU(2)表示((L_1，L_2)=(1，1)，即q=1/2，i=1/2)中不会发生相变。这是由于SU(2)禁闭机制阻止了退禁闭相变，即使在Rheta=pi.实作用通过重整化群变换接近“热核”类型.我们还用Rheta项进行了4维Z_N理论，这很有趣，因为它与“对偶”和“斜禁闭”有关(Imachi，Liu和Yoneyama)，2)N>2的CP^&lt；N-1&gt的数值研究(Imachi，Kanou和Yoneyama)。

项目成果

M, Imachi, etal: "Renormalization Group Analysis of U(2) Gauge Theary with θ-Term in 2Dimensions" Prog Theor Phys.97,5. 791-808 (1997)

M，Imachi 等人：“二维 θ 项的 U(2) 规范理论的重正化群分析”Prog Theor Phys.97,5 (1997)。

M.Imachi, T.Kakitsuka, N.Tsuzuki and H.Yoneyama: "Renormalization Group Analysis of U (2) Gauge Theory with rheta-term in 2 Dimensions" Prog.Theor.Phys.97. 791-808 (1997)

M.Imachi、T.Kakitsuka、N.Tsuzuki 和 H.Yoneyama：“二维 U (2) 规范理论与 rheta 项的重整化群分析”Prog.Theor.Phys.97。

M.Imachi, et al: "Renormatization Group Analysis of U (2) Gange Theory with θ Term in 2 Dimensions" Prog. Theor. Phys.97・5. 791-808 (1997)

M.Imachi 等人：“二维 θ 项的 U (2) Gange 理论的重整群分析”Prog. 791-808 (1997)。