  Little String Theory (LST) is a still somewhat mysterious theory that
describes the dynamics near a certain class of time-like singularities in
string theory. In this paper we discuss the topological version of LST, which
describes topological strings near these singularities. For 5+1 dimensional
LSTs with sixteen supercharges, the topological version may be described
holographically in terms of the N=4 topological string (or the N=2 string) on
the transverse part of the near-horizon geometry of NS5-branes. We show that
this topological string can be used to efficiently compute the half-BPS F^4
terms in the low-energy effective action of the LST. Using the strong-weak
coupling string duality relating type IIA strings on K3 and heterotic strings
on T^4, the same terms may also be computed in the heterotic string near a
point of enhanced gauge symmetry. We study the F^4 terms in the heterotic
string and in the LST, and show that they have the same structure, and that
they agree in the cases for which we compute both of them. We also clarify some
additional issues, such as the definition and role of normalizable modes in
holographic linear dilaton backgrounds, the precise identifications of vertex
operators in these backgrounds with states and operators in the supersymmetric
Yang-Mills theory that arises in the low energy limit of LST, and the
normalization of two-point functions.
