Self-Duality and Self-Similarity of Little String Orbifolds

Abstract

We study a class of $\mathcal{N}=(1,0)$ little string theories obtained from orbifolds of M-brane configurations. These are realised in two different ways that are dual to each other: either as $M$ parallel M5-branes probing a transverse $A_{N-1}$ singularity or $N$ M5-branes probing an $A_{M-1}$ singularity. These backgrounds can further be dualised into toric, non-compact Calabi-Yau threefolds $X_{N,M}$ which have double elliptic fibrations and thus give a natural geometric description of T-duality of the little string theories. The little string partition functions are captured by the topological string partition function of $X_{N,M}$. We analyse in detail the free energies ${\Sigma }_{N,M}$ associated with the latter in a special region in the Kähler moduli space of $X_{N,M}$ and discover a remarkable property: in the Nekrasov-Shatashvili-limit, ${\Sigma }_{N,M}$ is identical to $NM$ times ${\Sigma }_{1,1}$. This entails that the BPS degeneracies for any $(N,M)$ can uniquely be reconstructed from the $(N,M)=(1,1)$ configuration, a property we refer to as self-similarity. Moreover, as ${\Sigma }_{1,1}$ is known to display a number of recursive structures, BPS degeneracies of little string configurations for arbitrary $(N,M)$ as well acquire additional symmetries. These symmetries suggest that in this special region the two little string theories described above are self-dual under T-duality.

49 pages, 4 figures

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• Five-Dimensional Gauge Theories from Shifted Web Diagrams
• Bound States of Little Strings and Symmetric Orbifold CFTs
• Five-Brane Webs and Highest Weight Representations
• Dihedral Symmetries of Gauge Theories from Dual Calabi-Yau Threefolds
• E(lementary) Strings in Six-Dimensional Heterotic F-Theory
• 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
• Symmetries in A-Type Little String Theories, Part I
• Compactified Webs and Domain Wall Partition Functions
• Non-perturbative Symmetries of Little Strings and Affine Quiver Algebras
• Domain walls and M2-branes partition functions: M-theory and ABJM Theory