从de Wit-Nicolai结构走向新的膜流
Towards New Membrane Flow from de Wit-Nicolai Construction
摘要：
1986年，de Wit和Nicolai构造了具有7维指数的4型内场强。它们由以下六个量确定：四维N=8规范超引力的56个bein，圆形七球上的Killing矢量，作用于这些Killing矢量的协变导数，翘曲因子，具有四维指数的场强和7维度规。本文通过投影出自旋为1/2的费米子扇区变分中出现的SU（8）张量中剩余的混合4-形式场强，也将它们用上述某些量明确地表示出来。对于已知的临界点，N=8 SO（8）点和非超对称SO（7）^{+}点，我们通过计算全非线性表达式再现了相应的11维隆起。此外，我们还得到了非超对称SO（7）^{+}不变流的11维提升.我们首次破译了它们的隐式公式，并将提供如何在11维中获得新的超对称或非超对称膜流。
英文摘要：
The internal 4-form field strengths with 7-dimensional indices have been constructed by de Wit and Nicolai in 1986. They are determined by the following six quantities: the 56-bein of 4-dimensional N=8 gauged supergravity, the Killing vectors on the round seven-sphere, the covariant derivative acting on these Killing vectors, the warp factor, the field strengths with 4-dimensional indices and the 7-dimensional metric. In this paper, by projecting out the remaining mixed 4-form field strengths in an SU(8) tensor that appears in the variation of spin 1/2 fermionic sector, we also write down them explicitly in terms of some of the above quantities. For the known critical points, the N=8 SO(8) point and the nonsupersymmetric SO(7)^{+} point, we reproduce the corresponding 11-dimensional uplifts by computing the full nonlinear expressions. Moreover, we find out the 11-dimensional lift of the nonsupersymmetric SO(7)^{+} invariant flow. We decode their implicit formula for the first time and the present work will provide how to obtain the new supersymmetric or nonsupersymmetric membrane flows in 11-dimensions.
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