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arXiv 1003.5018hep-thgr-qc
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N=8超引力中反项的一种简单方法

A simple approach to counterterms in N=8 supergravity

Henriette Elvang, Daniel Z. Freedman, Michael Kiermaier

备注：
25 pages, 1 figure, published version
发表信息：
JHEP 1011:016,2010
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摘要：

我们提出了一个简单的系统方法来研究N=8超引力中的候选反项。我们避免了反项算子的复杂细节，因为我们使用它们产生的壳层上矩阵元。所有的n点矩阵元素的一个独立的超对称不变算子的形式D^{2k} R^n +.必须是局部的并且满足超对称沃德恒等式。这些都是很强的约束，我们直接测试是否可以构建具有这些属性的矩阵元素。如果不是，则该算子不具有超对称化，并且它被排除为潜在的反项。当n>4时，我们发现R^n、D^2 R^n、D^4 R^n和D^6 R^n作为MHV振幅的反项被排除，而在NMHV水平上只有R^n和D^2 R^n被排除。因此，对于循环阶数L<7，不存在独立的D^{2k}R^n对应项，其中n>4。如果不排除一个算子，我们的方法构造一个明确的超级振幅的矩阵元素。这是在NMHV水平和其他情况下对7圈D^4 R^6算子进行的。我们还开始研究没有领先的纯引力子矩阵元素，它可以发生在MHV水平以外的反项。排除/允许的候选反项的情况汇总在一个彩色图表中。

英文摘要：

We present a simple systematic method to study candidate counterterms in N=8 supergravity. Complicated details of the counterterm operators are avoided because we work with the on-shell matrix elements they produce. All n-point matrix elements of an independent SUSY invariant operator of the form D^{2k} R^n +... must be local and satisfy SUSY Ward identities. These are strong constraints, and we test directly whether or not matrix elements with these properties can be constructed. If not, then the operator does not have a supersymmetrization, and it is excluded as a potential counterterm. For n>4, we find that R^n, D^2 R^n, D^4 R^n, and D^6 R^n are excluded as counterterms of MHV amplitudes, while only R^n and D^2 R^n are excluded at the NMHV level. As a consequence, for loop order L<7, there are no independent D^{2k}R^n counterterms with n>4. If an operator is not ruled out, our method constructs an explicit superamplitude for its matrix elements. This is done for the 7-loop D^4 R^6 operator at the NMHV level and in other cases. We also initiate the study of counterterms without leading pure-graviton matrix elements, which can occur beyond the MHV level. The landscape of excluded/allowed candidate counterterms is summarized in a colorful chart.

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