TY - JOUR

T1 - The SL(K+3,C) symmetry of the bosonic string scattering amplitudes

AU - Lai, Sheng Hong

AU - Lee, Jen-Chi

AU - Yang, Yi

PY - 2019/4

Y1 - 2019/4

N2 - We discover that 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 can be expressed in terms of the basis functions in the infinite dimensional representation space of the SL(K+3,C) group. In addition, we find that the K+2 recurrence relations among the LSSA discovered by the present authors previously can be used to reproduce the Cartan subalgebra and simple root system of the SL(K+3,C) group with rank K+2. As a result, 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 SL(K+3,C) group can be used to directly prove Gross conjecture [1–3], which was previously corrected and proved by the method of decoupling of zero norm states [4–10].

AB - We discover that 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 can be expressed in terms of the basis functions in the infinite dimensional representation space of the SL(K+3,C) group. In addition, we find that the K+2 recurrence relations among the LSSA discovered by the present authors previously can be used to reproduce the Cartan subalgebra and simple root system of the SL(K+3,C) group with rank K+2. As a result, 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 SL(K+3,C) group can be used to directly prove Gross conjecture [1–3], which was previously corrected and proved by the method of decoupling of zero norm states [4–10].

UR - http://www.scopus.com/inward/record.url?scp=85061994793&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2019.02.013

DO - 10.1016/j.nuclphysb.2019.02.013

M3 - Article

AN - SCOPUS:85061994793

VL - 941

SP - 53

EP - 71

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -