Recurrence relations of Kummer functions and Regge string scattering amplitudes

Abstract

We discover an infinite number of recurrence relations among Regge string scattering amplitudes \cite{bosonic,RRsusy} of different string states at arbitrary mass levels in the open bosonic string theory. As a result, all Regge string scattering amplitudes can be algebraically solved up to multiplicative factors. Instead of decoupling zero-norm states in the fixed angle regime, the calculation is based on recurrence relations and addition theorem of Kummer functions of the second kind. These recurrence relations among Regge string scattering amplitudes are dual to linear relations or symmetries among high-energy fixed angle string scattering amplitudes discovered previously.

26 pages,v2:28 pages,three paragraphs after Eq.(3.83) added

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Cited by in corpus (8)

• Classical Limit of Higher-Spin String Amplitudes
• The Lauricella Functions and Exact String Scattering Amplitudes
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• Solving Lauricella String Scattering Amplitudes through Recurrence Relations
• To see Symmetry in a Forest of Trees
• Recent developments of the Lauricella string scattering amplitudes and their exact SL(K+3,C) Symmetry
• Recurrence Relations of Higher Spin BPST Vertex Operators for Open String
• The String BCJ Relations Revisited and Extended Recurrence relations of Nonrelativistic String Scattering Amplitudes