On The Universality Class Of Little String Theories

TL;DR

This work treats Little String Theories (LSTs) in six dimensions as quasilocal quantum field theories, where Wightman functions grow exponentially in momentum space and strictly local observables do not exist. By adopting Jaffe’s non-tempered test-function spaces with $g(t)=e^{\sqrt t}$, the authors formulate a framework in which AL (approximately local) observables can exist only for regions larger than a frame-dependent length $\ell$, conjectured to be $\ell \sim {\sqrt N}/{M_s}$. They introduce strong quasilocality as a robust axiom guaranteeing near-local behavior at long distances, show that weak CPT and spin-statistics theorems can hold, and provide a Gaussian quasilocal QFT as an explicit example. The analysis links exponential growth in Wightman functions to the nonlocality of LSTs while preserving much of the local QFT structure in the infrared, and it discusses T-duality, holography, and possible applications to string-theoretic nonlocal phenomena. Overall, the paper proposes a coherent nonlocal QFT paradigm for LSTs that accommodates noncompactly supported test functions, frame-dependent localization, and a calculable minimal observable length scale.

Abstract

We propose that Little String Theories in six dimensions are quasilocal quantum field theories. Such field theories obey a modification of Wightman axioms which allows Wightman functions (i.e. vacuum expectation values of products of fundamental fields) to grow exponentially in momentum space. Wightman functions of quasilocal fields in x-space violate microlocality at short distances. With additional assumptions about the ultraviolet behavior of quasilocal fields, one can define approximately local observables associated to big enough compact regions. The minimum size of such a region can be interpreted as the minimum distance which observables can probe. We argue that for Little String Theories this distance is of order {\sqrt N}/M_s.