Stringy scaling of n-point hard string scattering amplitudes

Abstract Motivated by the recent calculation of the SL $$(K+3,\mathbb {C})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>K</mml:mi> <mml:mo>+</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mi>C</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> symmetry of n -point Lauricella string scattering amplitudes (SSA) of open bosonic string theory, we calculate ratios of the solvable infinite linear relations of arbitrary n -point hard SSA (HSSA). We discover a general stringy scaling behavior for all n -point HSSA to all string loop orders. For the special case of $$n=4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> , the stringy scaling behavior reduces to the infinite linear relations and constant ratios among HSSA conjectured by Gross (Phys Rev Lett 60:1229, 1988) and later corrected and calculated by the method of decoupling of zero-norm states (Chan et al. in Phys Rev Lett 96(17): 171601, 2006).