$(\alpha')^4$ Corrections in Holographic Large N_c QCD and $\pi - \pi$ Scattering

We calculate the ${\alpha'}^4$ corrections to the non-Abelian DBI action on the D8-brane in the holographic dual of large N_c QCD proposed by Sakai and Sugimoto. These give rise to higher derivative terms, in particular, four derivative contact terms for the pion field with the coupling uniquely determined. We calculate the pion-pion scattering amplitude near threshold. The results respecting unitarity are in qualitative agreement with the experimental curves.
Comment: Latex, 13 pages, 1 figure, Text enlarged, two tables introduced, one more curve is added in the figure, added more references