LSZ in LST

TL;DR

This paper analyzes the analytic structure of off-shell correlation functions in Little String Theories, revealing pole structures and their physical implications, and connects these findings to low-energy gauge theories and string theory phenomena.

Contribution

It provides a detailed analysis of the pole structure of correlation functions in LSTs and clarifies their physical interpretation, including implications for gauge theories and string phases.

Findings

n-point functions have single poles corresponding to localized states

additional poles indicate UV/IR mixing effects

results clarify low-energy Green function behavior

Abstract

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.