从ABJM看M理论中$D^4 R^4$的缺失
Absence of $D^4 R^4$ in M-Theory From ABJM
摘要：
超对称性允许M理论中的$D^4 R^4$相互作用，但这样的相互作用与弦理论的对偶性不一致，因此已知是不存在的。利用ABJM理论计算了11维超引力子的四点散射振幅，给出了不存在$D^4 R^4$ M理论相互作用的新证明.该计算将先前执行的计算扩展到对应于$R^4$相互作用的顺序。在此扩展的新成分是解释的质量变形$S^3$配分函数的ABJM理论，这可以确定使用超对称本地化，作为一个约束梅林振幅与应力张量多重4点函数。作为此计算的一部分，我们涉及的4点函数的超共形主要的应力张量多重态的任何3D ${\cal N} = 8$ SCFT的一些4点函数的超共形后代。我们还提供了一个简洁的公式，一般集成4点功能的$S^d$的任何$d$。
英文摘要：
Supersymmetry allows a $D^4 R^4$ interaction in M-theory, but such an interaction is inconsistent with string theory dualities and so is known to be absent. We provide a novel proof of the absence of the $D^4 R^4$ M-theory interaction by calculating 4-point scattering amplitudes of 11d supergravitons from ABJM theory. This calculation extends a previous calculation performed to the order corresponding to the $R^4$ interaction. The new ingredient in this extension is the interpretation of the fourth derivative of the mass deformed $S^3$ partition function of ABJM theory, which can be determined using supersymmetric localization, as a constraint on the Mellin amplitude associated with the stress tensor multiplet 4-point function. As part of this computation, we relate the 4-point function of the superconformal primary of the stress tensor multiplet of any 3d ${\cal N} = 8$ SCFT to some of the 4-point functions of its superconformal descendants. We also provide a concise formula for a general integrated 4-point function on $S^d$ for any $d$.
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