arXiv 1502.052582015-02hep-th

玻色弦中引力子、声子和Kalb-Ramond场的软定理

Soft theorem for the graviton, dilaton and the Kalb-Ramond field in the bosonic string

Paolo Di Vecchia, Raffaele Marotta, Matin Mojaza

备注：: 17 pages + 10 pages Appendix. Several clarifying comments added in this version

摘要：

本文研究了玻色弦在软无质量态（引力子、激子和Kalb-Ramond反对称张量）和闭弦快子或其它闭弦无质量态中的散射振幅的行为。对于软引力子，我们确认了参考文献[24]中仅使用规范不变性获得的结果，对于外部快子，直到${\cal O}(q^1)$项，对于外部无质量闭弦态，直到${\cal O} (q^0)$项。此外，我们还导出了当声子场或Kalb-Ramond场变软时的散射振幅的行为。这些结果是新的，据我们所知，不能用规范不变性导出。结果表明，在所考察的情况下，引力子或反对称张量的软振幅是通过用它们各自的极化张量饱和张量$M_{μν}$而获得的，该张量是从引力子的规范不变性导出的。因此，在软扩展的情况下可能出现在$M_{μν}$中的额外项实际上不会出现。

英文摘要：

We study the behavior of the scattering amplitudes of the bosonic string involving a soft massless state (graviton, dilaton and Kalb-Ramond antisymmetric tensor) and closed string tachyons or other closed string massless states. For a soft graviton we confirm the results, obtained in Ref. [24] using just gauge invariance, up to terms of ${\cal O}(q^1)$ for external tachyons and up to terms of ${\cal O} (q^0)$ for external massless closed string states. Furthermore, we also derive the behavior of the scattering amplitude when a dilaton or a Kalb-Ramond field becomes soft. These results are new and cannot, to our knowledge, be derived by using gauge invariance. It turns out, in the cases examined, that the soft amplitude for a dilaton or for an antisymmetric tensor is obtained by saturating the tensor, $M_{μν}$, derived from gauge invariance for gravitons, with their respective polarization tensors. Thus extra terms that could have appeared in $M_{μν}$ in the case of a soft dilaton, in fact do not appear.

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