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 $(\frac{NM}{k},k)$ 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.

69 pages

References in corpus (4)

• Multiple Fibrations in Calabi-Yau Geometry and String Dualities
• Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds
• F-theory and Unpaired Tensors in 6D SCFTs and LSTs
• Little String Origin of Surface Defects

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• Triality in Little String Theories
• Dual Little Strings and their Partition Functions
• From Little String Free Energies Towards Modular Graph Functions
• Beyond Triality: Dual Quiver Gauge Theories and Little String Theories
• Five-Dimensional Gauge Theories from Shifted Web Diagrams
• Little strings on $D_n$ orbifolds
• M5 branes and Theta Functions
• Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants
• Five-Brane Webs and Highest Weight Representations
• Dihedral Symmetries of Gauge Theories from Dual Calabi-Yau Threefolds
• The ABCDEFG of Little Strings
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Symmetric Orbifold Theories from Little String Residues
• $DE$-type little strings from glued brane webs
• Non-perturbative Symmetries of Little Strings and Affine Quiver Algebras