SYM theory hard scattering from the dilaton-dilatino superstring scattering amplitude

We calculate the hard-scattering amplitude of bosonic states created by <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi mathvariant="script">O</a:mi><a:mi>k</a:mi><a:mrow><a:mo stretchy="false">(</a:mo><a:mn>8</a:mn><a:mo stretchy="false">)</a:mo></a:mrow></a:msubsup></a:math> operators and fermionic states created by <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msubsup><f:mi mathvariant="script">O</f:mi><f:msup><f:mi>k</f:mi><f:mo>′</f:mo></f:msup><f:mrow><f:mo stretchy="false">(</f:mo><f:mn>6</f:mn><f:mo stretchy="false">)</f:mo></f:mrow></f:msubsup></f:math> operators of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi mathvariant="script">N</k:mi><k:mo>=</k:mo><k:mn>4</k:mn></k:math> SYM theory from the dilaton-dilatino closed-string scattering amplitude in type IIB superstring theory, in the framework of the gauge/string theory duality considering a hard-wall model. These are single-trace operators of the <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>S</n:mi><n:mi>U</n:mi><n:mo stretchy="false">(</n:mo><n:msub><n:mi>N</n:mi><n:mi>c</n:mi></n:msub><n:mo stretchy="false">)</n:mo></n:math> <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi mathvariant="script">N</r:mi><r:mo>=</r:mo><r:mn>4</r:mn></r:math> SYM theory in four dimensions. We investigate the high-energy scaling at fixed angle and also in the Regge limit. We derive the leading and subleading terms contributing to the scattering cross section. This dual calculation of the hard-scattering amplitude is particularly interesting since it involves the scattering of two different types of external states. We calculate explicitly some angular integrals for two scalar spherical harmonics and two spinor spherical harmonics on the five-sphere, leading to selection rules.