  We discuss the analytic structure of off-shell correlation functions in
Little String Theories (LSTs) using their description as asymptotically linear
dilaton backgrounds of string theory. We focus on specific points in the LST
moduli space where this description involves the spacetime (R^{d-1,1} times
SL(2)/U(1) times a compact CFT), though we expect our qualitative results to be
much more general. We show that n-point functions of vertex operators O(p) have
single poles as a function of the d-dimensional momentum p, which correspond to
normalizable states localized near the tip of the SL(2)/U(1) cigar. Additional
poles arise due to the non-trivial dynamics in the bulk of the cigar, and these
can lead to a type of UV/IR mixing. Our results explain some previously
puzzling features of the low energy behavior of the Green functions. As another
application, we compute the precise combinations of single-trace and
multi-trace operators in the low-energy gauge theory which map to single string
vertex operators in the N=(1,1) supersymmetric d=6 LST. We also discuss the
implications of our results for two dimensional string theories and for the
(non-existence of a) Hagedorn phase transition in LSTs.

High Energy Physics - Theory