arXiv 1407.33702014-07hep-thmath.GR

对称空间上的积分群作用与超引力理论的离散对偶对称性

Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories

Lisa Carbone, Scott H. Murray, Hisham Sati

DOI：: 10.1063/1.4929538

摘要：

对于$G(\mathbb{R})$（一个秩为$n$的可裂单连通半单李群）和$K$（一个极大紧子群），利用Chevalley生成元和Steinberg表示，给出了计算$G/K$的Iwasawa坐标的方法.当$G/K$是超引力理论在$\geq 3$维中的标量陪集时，我们确定了积分形式$G(\mathbb{Z})$对$G/K$的作用.给出了10维IIB型超引力和$D=4$维11维超引力的离散$U$--对偶群$SL_2(\mathbb{Z})$和$E_7(\mathbb{Z})$在标量陪集$SL_2(\mathbb{R})/SO_2(\mathbb{R})$和$E_{7(+7)}(\mathbb{R})/[SU(8,\mathbb{R})/\{\pm Id\}]$上的作用量的显式结果.对于前者，我们用它来确定离散的U-对偶变换的标量部门的Borel规范，我们描述的离散对称性的双子电荷晶格。在经典水平上确定了$D=10$维中IIB型超引力基本BPS孤子的谱生成对称群，并提出了量子水平上这种对称的一个模拟。我们表明我们的方法可以用来研究一般的离散U-对偶群的轨道。

英文摘要：

For $G(\mathbb{R})$ a split, simply connected, semisimple Lie group of rank $n$ and $K$ the maximal compact subgroup of $G$, we give a method for computing Iwasawa coordinates of $G/K$ using the Chevalley generators and the Steinberg presentation. When $G/K$ is a scalar coset for a supergravity theory in dimensions $\geq 3$, we determine the action of the integral form $G(\mathbb{Z})$ on $G/K$. We give explicit results for the action of the discrete $U$--duality groups $SL_2(\mathbb{Z})$ and $E_7(\mathbb{Z})$ on the scalar cosets $SL_2(\mathbb{R})/SO_2(\mathbb{R})$ and $E_{7(+7)}(\mathbb{R})/[SU(8,\mathbb{R})/\{\pm Id\}]$ for type IIB supergravity in ten dimensions and 11--dimensional supergravity in $D=4$ dimensions, respectively. For the former, we use this to determine the discrete U--duality transformations on the scalar sector in the Borel gauge and we describe the discrete symmetries of the dyonic charge lattice. We determine the spectrum--generating symmetry group for fundamental BPS solitons of type IIB supergravity in $D=10$ dimensions at the classical level and we propose an analog of this symmetry at the quantum level. We indicate how our methods can be used to study the orbits of discrete U--duality groups in general.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文