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arXiv 1012.5797hep-th
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异常减少

Exceptional Reductions

Alessio Marrani, Emanuele Orazi, Fabio Riccioni

备注：
1+29 pages, 2 Tables; v2: minor amendment in caption of Table 1, Refs. added and updated; accepted for publication in J. Phys. A: Math. Theor
发表信息：
J.Phys.A44:155207,2011
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摘要：

从群E8的基本恒等式出发，我们进行逐步约化，即关于E7 xSU（2）和E6 xU（1）的最大和对称嵌入的分解。这一过程提供了一个系统的方法，涉及不变的原始张量结构的各种不可逆的基本恒等式。有限维例外李群我们得到新的身份E7和E6，突出E8的起源，一些众所周知的。为了阐明这种形式主义与基于对称标量流形的四维麦克斯韦-爱因斯坦超引力理论的联系（与不可约的欧几里德约当代数有关，唯一的例外是试探对称N = 2 stu模型），我们导出了一个涉及0-膜电荷辛不重复的唯一秩4对称不变张量的基本恒等式。U-对偶群的量子化，在超引力理论的电荷轨道量子化以及其中的多中心黑洞解研究中具有潜在的应用。

英文摘要：

Starting from basic identities of the group E8, we perform progressive reductions, namely decompositions with respect to the maximal and symmetric embeddings of E7xSU(2) and then of E6xU(1). This procedure provides a systematic approach to the basic identities involving invariant primitive tensor structures of various irreprs. of finite-dimensional exceptional Lie groups. We derive novel identities for E7 and E6, highlighting the E8 origin of some well known ones. In order to elucidate the connections of this formalism to four-dimensional Maxwell-Einstein supergravity theories based on symmetric scalar manifolds (and related to irreducible Euclidean Jordan algebras, the unique exception being the triality-symmetric N = 2 stu model), we then derive a fundamental identity involving the unique rank-4 symmetric invariant tensor of the 0-brane charge symplectic irrepr. of U-duality groups, with potential applications in the quantization of the charge orbits of supergravity theories, as well as in the study of multi-center black hole solutions therein.

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