Dual little strings from F-theory and flop transitions

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 string theories. (c) The Authors.5611Nsciescopu