Abstract
A particular two-parameter class of little string theories can be described by M parallel M5-branes probing a transverse affine AN − 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 left(frac{NM}{k},kright) 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 compactifications on toric, non-compact Calabi-Yau threefolds XN,M which have a double elliptic fibration 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 flop transitions. By working out the full duality map, we provide a simple check at the level of the free energy of little string theories.
Highlights
Little string theories are a class of interacting, non-local, ultraviolet complete quantum theories in six dimensions, which has a well-defined energy-momentum tensor
By working out the full duality map, we provide a simple check at the level of the free energy of little string theories
Denoting by ZI(INa,M) and ZI(IMb,N) the little string partition functions and by ZXN,M (t, T, m, 1,2) the refined topological string partition function1 on XN,M, we proposed in the previous work [10]
Summary
Little string theories are a class of interacting, non-local, ultraviolet complete quantum theories in six dimensions (or lower), which has a well-defined energy-momentum tensor. ZM orbifold of IIb little string theory of type AN−1: This little string theory generically preserves N = (1, 0) supersymmetry and is described through the decoupling limit of N NS5-branes in type IIA string theory probing an R4/ZM orbifold background. Extending the discussion in [26], the type IIb orbifolded little string theory can be described as a decoupling limit of N parallel NS5-branes that probe an affine AM−1 ALE space. The description we will mostly focus on in this paper, is in terms of F-theory on a two-parameter class of toric, non-compact Calabi-Yau threefolds XN,M , generalising the geometric approach to the little string theories with sixteen supercharges mentioned above.
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