  We study up to 8-derivative terms in the Coulomb branch effective action of
(1,1) little string theory, by collecting results of 4-gluon scattering
amplitudes from both perturbative 6D super-Yang-Mills theory up to 4-loop
order, and tree-level double scaled little string theory (DSLST). In previous
work we have matched the 6-derivative term from the 6D gauge theory to DSLST,
indicating that this term is protected on the entire Coulomb branch. The
8-derivative term, on the other hand, is unprotected. In this paper we compute
the 8-derivative term by interpolating from the two limits, near the origin and
near the infinity on the Coulomb branch, numerically from SU(k) SYM and DSLST
respectively, for k=2,3,4,5. We discuss the implication of this result on the
UV completion of 6D SYM as well as the strong coupling completion of DSLST. We
also comment on analogous interpolating functions in the Coulomb phase of
circle-compactified (2,0) little string theory.
