A magic pyramid of supergravities
A magic pyramid of supergravities
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DOI：
10.1007/jhep04(2014)178
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发表时间：
2014-04-29
影响因子：
5.4
通讯作者：
Nagy, S.
中科院分区：
文献类型：
--
作者：
Anastasiou, A.;Borsten, L.;Nagy, S.
通过用一个拉格朗日量和一组变换规则来表示N = 1，2，4，8，D = 3，Yang-Mills，但场的值分别为，最近证明了张量左和右多重态产生D = 3超引力的Freudenthal-Rosenfeld-Tits幻方。这随后与更熟悉的时空的R，C，H，O描述联系起来，给出了D = 3，4，6，10中扩展的超杨-米尔斯的统一的除法代数描述。在这里，这些结构聚集在一起，形成了一个神奇的超重力金字塔。D = 3的金字塔底部是已知的4 × 4幻方，而更高的层次是由D = 4的3 × 3正方形，D = 6的2 × 2正方形和D = 10的顶点II型超重力组成。相应的U-对偶群由一个新的代数结构给出，魔金字塔公式，它可以被认为是定义在三个除代数上，一个用于时空和每个左/右杨-米尔斯多重态。通过张量D = 3，4，6中的共形超多重态，我们还构造了一个共形魔金字塔. D = 10中的缺失项暗示了具有G/H对偶结构F-4（4）/Sp（3）x Sp（1）的奇异理论。
By formulating N = 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and single set of transformation rules, but with fields valued respectively in , it was recently shown that tensoring left and right multiplets yields a Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities. This was subsequently tied in with the more familiar R, C, H, O description of spacetime to give a unified division-algebraic description of extended super Yang-Mills in D = 3, 4, 6, 10. Here, these constructions are brought together resulting in a magic pyramid of supergravities. The base of the pyramid in D = 3 is the known 4 x 4 magic square, while the higher levels are comprised of a 3 x 3 square in D = 4, a 2 x 2 square in D = 6 and Type II supergravity at the apex in D = 10. The corresponding U-duality groups are given by a new algebraic structure, the magic pyramid formula, which may be regarded as being defined over three division algebras, one for spacetime and each of the left/right Yang-Mills multiplets. We also construct a conformal magic pyramid by tensoring conformal supermultiplets in D = 3, 4, 6. The missing entry in D = 10 is suggestive of anexotic theory with G/H duality structure F-4(4)/Sp(3) x Sp(1).