Dual Little Strings from F-Theory and Flop Transitions

Abstract : A particular two-parameter class of little string theories can be described by $M$ parallel M5-branes probing a transverse affine $A_{N-1}$ 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 $(\tfrac{NM}{k},k)$ are dual to each other, where $k=\text{gcd}(N,M)$. To argue for this duality, we use a geometric realization of these little string theories in terms of F-theory compactifications on toric, non-compact Calabi-Yau threefolds $X_{N,M}$ which have a double elliptic fibration structure. We show explicitly for a number of examples that $X_{NM/k,k}$ is part of the extended moduli space of $X_{N,M}$, i.e. the two are related through symmetry transformations and flop transitions. By working out the full duality map, we provide a simple check at the level of the free energy of the little string theories.
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S. Hohenegger, A. Iqbal, Soo-Jong Rey. Dual Little Strings from F-Theory and Flop Transitions. Journal of High Energy Physics, Springer Verlag (Germany), 2017, 2017 (7), pp.112. ⟨10.1007/JHEP07(2017)112⟩. ⟨in2p3-01388429⟩

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