Dual Little Strings from F-Theory and Flop Transitions

TL;DR

This paper explores dualities among a class of little string theories realized via M5-branes and F-theory, revealing a larger web of interconnected theories through geometric and flop transition analyses.

Contribution

It proposes a new duality between theories labeled by (N,M) and (NM/k,k), extending known dualities and supported by geometric and free energy calculations.

Findings

Identification of a larger web of dual little string theories.

Explicit geometric realization of dualities via Calabi-Yau threefolds.

Validation of dualities through free energy comparisons.

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.