Dual Little Strings and their Partition Functions

Abstract

We study the topological string partition function of a class of toric, double elliptically fibered Calabi-Yau threefolds $X_{N,M}$ at a generic point in the Kähler moduli space. These manifolds engineer little string theories in five dimensions or lower and are dual to stacks of M5-branes probing a transverse orbifold singularity. Using the refined topological vertex formalism, we explicitly calculate a generic building block which allows to compute the topological string partition function of $X_{N,M}$ as a series expansion in different Kähler parameters. Using this result we give further explicit proof for a duality found previously in the literature, which relates $X_{N,M}\sim X_{N^{\prime },M^{\prime }}$ for $NM=N^{\prime }{M}^{\prime }$ and $\text{gcd}(N,M)=\text{gcd}(N^{\prime },M^{\prime })$.

20 pages

References in corpus (4)

• The Refined Topological Vertex
• Flop invariance of the topological vertex
• Five-Brane Webs and Highest Weight Representations
• E(lementary) Strings in Six-Dimensional Heterotic F-Theory

Cited by in corpus (15)

• Universal Features of BPS Strings in Six-dimensional SCFTs
• Revisiting the classifications of 6d SCFTs and LSTs
• Triality in Little String Theories
• 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
• Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
• M5 branes and Theta Functions
• Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants
• 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
• Symmetries in A-Type Little String Theories, Part I
• Non-perturbative Symmetries of Little Strings and Affine Quiver Algebras