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arXiv 0903.4630hep-th
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光锥上的N=8超引力

N=8 Supergravity on the Light Cone

Renata Kallosh

摘要:

我们构造了手征动量超空间中光锥超场振幅的生成泛函。它产生的n-点粒子振幅在壳层上等价于协变振幅。基于依赖于无约束光锥手征标量超场的作用量,该泛函给出了Nair型振幅结构的正则d=4 QFT路径积分推导.通过对光锥手征坐标超空间进行傅立叶变换,我们发现,对于圈数小于n(n-1)/2 + 1的图,对具有n条腿的超场振幅的量子修正在横向上是非局域的.这表明了为什么UV无穷大,这是成比例的局部顶点,不能出现至少在7圈之前的光锥超图计算。结合E7对称性和超对称递归关系,我们认为光锥超图预言了d=4 N=8超引力的所有圈有限性。

英文摘要:

We construct the generating functional for the light-cone superfield amplitudes in a chiral momentum superspace. It generates the n-point particle amplitudes which on shell are equivalent to the covariant ones. Based on the action depending on unconstrained light-cone chiral scalar superfield, this functional provides a regular d=4 QFT path integral derivation of the Nair-type amplitude constructions. By performing a Fourier transform into the light-cone chiral coordinate superspace we find that the quantum corrections to the superfield amplitudes with n legs are non-local in transverse directions for the diagrams with the number of loops smaller than n(n-1)/2 +1. This suggests the reason why UV infinities, which are proportional to local vertices, cannot appear at least before 7 loops in the light-cone supergraph computations. By combining the E7 symmetry with the supersymmetric recursion relations we argue that the light-cone supergraphs predict all loop finiteness of d=4 N=8 supergravity.

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