  Little string theories (LSTs) are UV complete non-local 6D theories decoupled
from gravity in which there is an intrinsic string scale. In this paper we
present a systematic approach to the construction of supersymmetric LSTs via
the geometric phases of F-theory. Our central result is that all LSTs with more
than one tensor multiplet are obtained by a mild extension of 6D superconformal
field theories (SCFTs) in which the theory is supplemented by an additional,
non-dynamical tensor multiplet, analogous to adding an affine node to an ADE
quiver, resulting in a negative semidefinite Dirac pairing. We also show that
all 6D SCFTs naturally embed in an LST. Motivated by physical considerations,
we show that in geometries where we can verify the presence of two elliptic
fibrations, exchanging the roles of these fibrations amounts to T-duality in
the 6D theory compactified on a circle.
