JOURNAL OF HIGH ENERGY PHYSICS, v.2017, no.7, pp.112 -
A particular two-parameter class of little string theories can be described
by M parallel M5-branes probing a transverse ane AN1 singularity. We previously
discussed the duality between the theories labelled by (N;M) and (M;N). In this work,
we propose that these two are in fact only part of a larger web of dual theories. We provide
evidence that the theories labelled by (N;M) and (NM
k ; k) are dual to each other, where
k = gcd(N;M). To argue for this duality, we use a geometric realization of these little
string theories in terms of F-theory compactications on toric, non-compact Calabi-Yau
threefolds XN;M which have a double elliptic bration structure. We show explicitly for
a number of examples that XNM=k;k is part of the extended moduli space of XN;M , i.e.
the two are related through symmetry transformations and
op transitions. By working
out the full duality map, we provide a simple check at the level of the free energy of little
(c) The Authors.