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arXiv 2012.14726hep-th
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Lauricella弦散射振幅及其精确SL(K+3,C)对称性的最新进展

Recent developments of the Lauricella string scattering amplitudes and their exact SL(K+3,C) Symmetry

Sheng-Hong Lai, Jen-Chi Lee, Yi Yang

摘要:

本文提出了一个新的视角来论证Gross猜想在弦论高能对称性中的应用。在26维开放玻色弦论中,我们讨论了三个快子和一个任意弦态的精确弦散射振幅(SSA),即劳里切拉散射振幅(LSSA)的构造。这些LSSA形成SL(K+3,C)群的无限维表示。此外,我们证明了SL(K+3,C)群可以用来解决所有的LSSA,并表示为一个振幅。作为在硬散射极限下的应用,LSSA可以直接证明Gross猜想,而Gross猜想是用零模态解耦(ZNS)方法修正和证明的。最后,利用精确的LSSA可以重新导出SL(5,C)对称性下Regge散射极限中SSA的递推关系,以及最近发现的SL(4,C)对称性下非相对论散射极限中SSA的推广递推关系(包括质量和自旋相关的弦BCJ关系).

英文摘要:

In this review we propose a new perspective to demonstrate Gross conjecture on high energy symmetry of string theory. We review the construction of the exact string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA (LSSA), in the 26D open bosonic string theory. These LSSA form an infinite dimensional representation of the SL(K+3,C) group. Moreover, we show that the SL(K+3,C) group can be used to solve all the LSSA and express them in terms of one amplitude. As an application in the hard scattering limit, the LSSA can be used to directly prove Gross conjecture which was previously corrected and proved by the method of decoupling of zero norm states (ZNS). Finally, the exact LSSA can be used to rederive the recurrence relations of SSA in the Regge scattering limit with associated SL(5,C) symmetry and the extended recurrence relations (including the mass and spin dependent string BCJ relations) in the nonrelativistic scattering limit with associated SL(4,C) symmetry discovered recently.

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