Recent Developments of the Lauricella String Scattering Amplitudes and Their Exact SL(K+3, C) Symmetry

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

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

1 Scopus citations


In this review, we propose a new perspective to demonstrate the Gross conjecture regarding the high-energy symmetry of string theory. We review the construction of the exact string scattering amplitudes (SSAs) of three tachyons and one arbitrary string state, or the Lauricella SSA (LSSA), in the 26D open bosonic string theory. These LSSAs 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 LSSAs and express them in terms of one amplitude. As an application in the hard scattering limit, the LSSA can be used to directly prove the Gross conjecture, which was previously corrected and proved by the method of the 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 the associated SL(4,C) symmetry discovered recently.

Original languageEnglish
Article number454
Number of pages37
Issue number3
StatePublished - Mar 2021


  • string scattering amplitudes
  • Lauricella function
  • symmetry

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